The document summarizes an experiment to measure the average lifespan of muons using a muon detector. The detector measured the time between a muon entering and decaying using a scintillation light and timing circuit. The average lifespan was calculated from the decay rate determined by the software. However, the calculated average lifespan was only 10% of the accepted value, indicating an error occurred during the experiment or calculations.
This document provides a summary of key developments in the foundations of quantum mechanics. It discusses Planck's discovery that led to defining Planck's constant h, which established that energy is quantized. Einstein's work on the photoelectric effect supported this and introduced the photon concept. Bohr used classical mechanics and energy quantization to develop his model of the hydrogen atom. The document outlines the revolutionary changes brought by quantum theory and its greater scope and applicability compared to classical physics. It provides context for understanding quantum mechanics from first principles.
Quantum mechanics describes the behavior of matter and light on the atomic and subatomic scale. Some key points of the quantum mechanics view are that particles can exhibit both wave-like and particle-like properties, their behavior is probabilistic rather than definite, and some properties like position and momentum cannot be known simultaneously with complete precision due to the Heisenberg uncertainty principle. Quantum mechanics has successfully explained various phenomena that classical physics could not and led to important technologies like lasers, MRI machines, and semiconductor devices.
Classical mechanics vs quantum mechanicsZahid Mehmood
Classical mechanics can explain motion based on Newton's laws of forces and particles. However, experiments at the atomic scale produced results inconsistent with classical theory. Max Planck explained blackbody radiation by quantizing electromagnetic radiation. Later, experiments showed matter also exhibits wave-particle duality, requiring new theories like quantum mechanics.
Particle in a box- Application of Schrodinger wave equationRawat DA Greatt
The document summarizes key concepts from quantum chemistry, including:
1) It introduces the historical development of quantum mechanics from classical mechanics and discusses how quantum theory was needed to describe atomic and subatomic phenomena.
2) It then summarizes the particle-like and wave-like properties of light and matter and introduces the Schrodinger equation.
3) The document concludes by presenting the particle-in-a-box model and explaining how solving the Schrodinger equation for this system shows that a particle's energy is quantized into discrete energy levels when confined in a box.
[1] Photoelectric effect provides evidence that light behaves as particles called photons, with each photon having energy hν. This explains the threshold frequency and instantaneous emission.
[2] Compton scattering demonstrates that photons transfer discrete packets of energy and momentum to electrons during collisions, with the photon's wavelength increasing in accordance with conservation laws. This provided direct evidence that photons are real particles.
[3] Pair production demonstrates that a photon's energy can be converted into an electron-positron pair, as predicted by Einstein's equation E=mc2. A minimum photon energy of 1.02 MeV is required to produce the pairs.
Basic and fundamental of quantum mechanics (Theory)Halavath Ramesh
Quantum mechanics arose in the early 20th century to explain experimental phenomena that classical mechanics could not, such as black body radiation and the photoelectric effect. The document discusses the origins and fundamental concepts of quantum mechanics, including the dual wave-particle nature of matter and light, the uncertainty principle, and Schrodinger's formulation of quantum mechanics using wave functions and his time-independent equation. It explains that wave functions provide probabilistic information about finding particles in particular regions rather than definite trajectories, replacing Bohr's orbital model.
Quantum mechanics is a new way of understanding the atomic world based on quanta or packets of energy. Light can behave as both a particle and a wave, with photons as quanta of light energy. The photoelectric effect and emission line spectra provided evidence that light behaves as quanta that can be absorbed or emitted in specific amounts of energy. Bohr's model of the hydrogen atom explained transitions between discrete energy levels by quantization of angular momentum and energy.
CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I
5.1 X-Ray Scattering (review and some more material)
5.2 De Broglie Waves
5.3 Electron Scattering / Transmission electron microscopy
5.4 Wave Motion
5.5 Waves or Particles?
5.6 Uncertainty Principle
5.7 Probability, Wave Functions, and the Copenhagen Interpretation
5.8 Particle in a Box
This document provides a summary of key developments in the foundations of quantum mechanics. It discusses Planck's discovery that led to defining Planck's constant h, which established that energy is quantized. Einstein's work on the photoelectric effect supported this and introduced the photon concept. Bohr used classical mechanics and energy quantization to develop his model of the hydrogen atom. The document outlines the revolutionary changes brought by quantum theory and its greater scope and applicability compared to classical physics. It provides context for understanding quantum mechanics from first principles.
Quantum mechanics describes the behavior of matter and light on the atomic and subatomic scale. Some key points of the quantum mechanics view are that particles can exhibit both wave-like and particle-like properties, their behavior is probabilistic rather than definite, and some properties like position and momentum cannot be known simultaneously with complete precision due to the Heisenberg uncertainty principle. Quantum mechanics has successfully explained various phenomena that classical physics could not and led to important technologies like lasers, MRI machines, and semiconductor devices.
Classical mechanics vs quantum mechanicsZahid Mehmood
Classical mechanics can explain motion based on Newton's laws of forces and particles. However, experiments at the atomic scale produced results inconsistent with classical theory. Max Planck explained blackbody radiation by quantizing electromagnetic radiation. Later, experiments showed matter also exhibits wave-particle duality, requiring new theories like quantum mechanics.
Particle in a box- Application of Schrodinger wave equationRawat DA Greatt
The document summarizes key concepts from quantum chemistry, including:
1) It introduces the historical development of quantum mechanics from classical mechanics and discusses how quantum theory was needed to describe atomic and subatomic phenomena.
2) It then summarizes the particle-like and wave-like properties of light and matter and introduces the Schrodinger equation.
3) The document concludes by presenting the particle-in-a-box model and explaining how solving the Schrodinger equation for this system shows that a particle's energy is quantized into discrete energy levels when confined in a box.
[1] Photoelectric effect provides evidence that light behaves as particles called photons, with each photon having energy hν. This explains the threshold frequency and instantaneous emission.
[2] Compton scattering demonstrates that photons transfer discrete packets of energy and momentum to electrons during collisions, with the photon's wavelength increasing in accordance with conservation laws. This provided direct evidence that photons are real particles.
[3] Pair production demonstrates that a photon's energy can be converted into an electron-positron pair, as predicted by Einstein's equation E=mc2. A minimum photon energy of 1.02 MeV is required to produce the pairs.
Basic and fundamental of quantum mechanics (Theory)Halavath Ramesh
Quantum mechanics arose in the early 20th century to explain experimental phenomena that classical mechanics could not, such as black body radiation and the photoelectric effect. The document discusses the origins and fundamental concepts of quantum mechanics, including the dual wave-particle nature of matter and light, the uncertainty principle, and Schrodinger's formulation of quantum mechanics using wave functions and his time-independent equation. It explains that wave functions provide probabilistic information about finding particles in particular regions rather than definite trajectories, replacing Bohr's orbital model.
Quantum mechanics is a new way of understanding the atomic world based on quanta or packets of energy. Light can behave as both a particle and a wave, with photons as quanta of light energy. The photoelectric effect and emission line spectra provided evidence that light behaves as quanta that can be absorbed or emitted in specific amounts of energy. Bohr's model of the hydrogen atom explained transitions between discrete energy levels by quantization of angular momentum and energy.
CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I
5.1 X-Ray Scattering (review and some more material)
5.2 De Broglie Waves
5.3 Electron Scattering / Transmission electron microscopy
5.4 Wave Motion
5.5 Waves or Particles?
5.6 Uncertainty Principle
5.7 Probability, Wave Functions, and the Copenhagen Interpretation
5.8 Particle in a Box
Quantum mechanics for Engineering StudentsPraveen Vaidya
The Quantum mechanics study material gives insight into the fundamentals of the modern theory of physics related to Heisenberg uncertainty principle, wavefunction, concepts of potential well etc.
12th Physics - Atoms Molecules and Nuclei for JEE Main 2014Ednexa
This document contains information about Thomson's atomic model, Rutherford's atomic model, and Bohr's atomic model. It discusses experiments that led to the development of these atomic models, such as Geiger and Marsden's gold foil experiment. The key points are:
1) Thomson proposed the earliest atomic model which had electrons distributed randomly in the atom.
2) Rutherford's gold foil experiment led him to propose the planetary model of the atom with a small, dense nucleus at the center.
3) Bohr improved upon Rutherford's model by incorporating Planck's quantum theory and proposing electron orbits and allowed energy levels. His model successfully explained atomic spectra.
This document summarizes several quantum mechanics methods for calculating molecular properties, including semi-empirical, density functional theory (DFT), and correlation methods. It discusses how semi-empirical methods approximate integrals to speed up calculations compared to Hartree-Fock. DFT is described as an alternative to wavefunction methods that uses the electron density. Popular DFT functionals and how they include exchange and correlation are outlined. Geometry optimization and vibrational frequency calculations are also summarized.
CHAPTER 10 Molecules and Solids
10.1 Molecular Bonding and Spectra
10.2 Stimulated Emission and Lasers
10.3 Structural Properties of Solids
10.4 Thermal and Magnetic Properties of Solids
10.5 Superconductivity
10.6 Applications of Superconductivity
3.1 Discovery of the X Ray and the Electron
3.2 Determination of Electron Charge
3.3 Line Spectra
3.4 Quantization
3.5 Blackbody Radiation
3.6 Photoelectric Effect
3.7 X-Ray Production
3.8 Compton Effect
3.9 Pair Production and Annihilation
Notes for Atoms Molecules and Nuclei - Part IIIEdnexa
- The document provides information about various topics in nuclear physics including de Broglie wavelength, composition and size of nucleus, isotopes, nuclear binding energy, radioactive decay, and nuclear fission.
- It defines key terms like isotopes, isobars, isotones, mass defect, nuclear binding energy, radioactive decay, half-life, decay constant, and describes the properties and characteristics of alpha particles, beta particles, and gamma rays.
- Mathematical relationships are given for radius of nucleus, mass defect, nuclear binding energy, radioactive decay law, and calculating half-life from the decay constant. Examples are provided to illustrate various concepts.
1. Quantum mechanics began with Max Planck's paper in 1900 explaining black body radiation. It extends physics to small dimensions and includes classical laws as special cases.
2. Photoelectric effect shows that light behaves as particles called photons. Einstein's equation explained it using the photon energy.
3. Compton scattering showed that photons can collide with and transfer energy to electrons. The Compton wavelength was derived from this.
The document discusses the development of quantum electrodynamics (QED) from its origins in Dirac's 1927 paper on the quantum theory of radiation. It provides an overview of the key topics covered in the subsequent chapters, including particles and fields, quantization of the electromagnetic field, Feynman diagrams, and renormalization in QED. The goal is to show how electrons and photons interact using quantum field theory by representing particles as excitations of underlying fields and developing perturbative techniques to calculate processes like scattering and radiation.
The document summarizes key details about the hydrogen atom and its electron orbital structure based on quantum mechanics. It provides:
1) A direct observation of the electron orbital of a hydrogen atom placed in an electric field, obtained through photoionization microscopy. Interference patterns observed directly reflect the nodal structure of the wavefunction.
2) Calculated and measured probability patterns for the electron in different energy levels of the hydrogen atom are shown. Bright regions correspond to high probability of finding the electron.
3) An overview of solving the radial, angular and azimuthal coordinate functions of the hydrogen atom through series expansion, as exact solutions have not been found. Approximate solutions can be obtained for more complex atoms like he
4.1 The Atomic Models of Thomson and Rutherford
4.2 Rutherford Scattering
4.3 The Classic Atomic Model
4.4 The Bohr Model of the Hydrogen Atom
4.5 Successes and Failures of the Bohr Model
4.6 Characteristic X-Ray Spectra and Atomic Number
4.7 Atomic Excitation by Electrons
Quantum mechanics provides a mathematical description of the wave-particle duality of matter and energy at small atomic and subatomic scales. It differs significantly from classical mechanics, as phenomena such as superconductivity cannot be explained using classical mechanics alone. Key aspects of quantum mechanics include wave-particle duality, the uncertainty principle, and discrete energy levels determined by Planck's constant and frequency.
The document discusses Quantum Electrodynamics and the interaction of light and matter. It explains key concepts like the Schrodinger equation, quantized energy levels, the Heisenberg Uncertainty Principle, Feynman diagrams, and the spontaneous creation and destruction of particles. While some aspects of quantum mechanics seem strange, the theories have been shown to be over 99.9999975% accurate in describing phenomena.
This document provides an overview of quantum mechanics concepts related to light and atomic structure. It discusses how light behaves as both a wave and particle, and introduces the electromagnetic spectrum. It then covers atomic structure concepts like electron configurations, energy levels, quantum numbers, and orbital shapes and filling diagrams. The document aims to explain how electrons are arranged in atoms and the underlying quantum mechanical principles.
Introduction to quantum mechanics and schrodinger equationGaurav Singh Gusain
Classical mechanics describes macroscopic objects while quantum mechanics describes microscopic objects due to limitations of classical theory. Quantum mechanics was introduced after classical mechanics failed to explain experimental observations involving microscopic particles. Some key aspects of quantum mechanics are the photoelectric effect, blackbody radiation, Compton effect, wave-particle duality, the Heisenberg uncertainty principle, and Schrodinger's wave equation. Schrodinger's equation describes the wave function and probability of finding a particle.
The document summarizes key concepts about the hydrogen atom from quantum mechanics. It begins by introducing the Schrödinger equation and how it can be applied and solved for the hydrogen atom potential. The solution involves separation of variables into radial, angular, and azimuthal components. This leads to the identification of three quantum numbers - principal (n), angular momentum (l), and magnetic (ml) - that characterize the possible energy states. Higher sections discuss properties like orbital shapes, spin, and transition selection rules between energy levels and electron probability distributions.
Quantum theory provides a framework to understand phenomena at the atomic scale that cannot be explained by classical physics. It proposes that energy is emitted and absorbed in discrete units called quanta. This explains observations like the photoelectric effect where electrons are only ejected above a threshold frequency. Light behaves as both a wave and particle - a photon. Similarly, matter exhibits wave-particle duality as demonstrated by electron diffraction. At the quantum level, only probabilities, not definite values, can be predicted. Quantum mechanics is applied to describe atomic structure and spectra.
Tyrrie Campbell is an experienced IT technician with over 10 years of experience in areas such as installation, networking, repairing, and supporting various systems. He has various technical certifications including A+, Net+, MCP, and ITIL training. He has worked in roles such as an IT instructor, HP engineer supporting blade systems and servers, service desk analyst, and technical support specialist for several companies. Campbell aims to utilize his extensive skills and experience to provide effective IT support.
This document summarizes outcomes from 100 fetal myelomeningocele (fMMC) repair procedures performed at the Children's Hospital of Philadelphia between 2011-2014. Key findings include:
- 29% of women evaluated were candidates for fMMC repair. The average gestational age at surgery was 23.4 weeks.
- Complications included membrane separation (23%), preterm premature rupture of membranes (32%), and preterm labor (38%).
- The average gestational age at delivery was 34.3 weeks. The perinatal loss rate was 6%, including 2 fetal demises and 4 neonatal deaths.
- 90.8% of women delivered at the hospital. 71% of neonates showed no
Quantum mechanics for Engineering StudentsPraveen Vaidya
The Quantum mechanics study material gives insight into the fundamentals of the modern theory of physics related to Heisenberg uncertainty principle, wavefunction, concepts of potential well etc.
12th Physics - Atoms Molecules and Nuclei for JEE Main 2014Ednexa
This document contains information about Thomson's atomic model, Rutherford's atomic model, and Bohr's atomic model. It discusses experiments that led to the development of these atomic models, such as Geiger and Marsden's gold foil experiment. The key points are:
1) Thomson proposed the earliest atomic model which had electrons distributed randomly in the atom.
2) Rutherford's gold foil experiment led him to propose the planetary model of the atom with a small, dense nucleus at the center.
3) Bohr improved upon Rutherford's model by incorporating Planck's quantum theory and proposing electron orbits and allowed energy levels. His model successfully explained atomic spectra.
This document summarizes several quantum mechanics methods for calculating molecular properties, including semi-empirical, density functional theory (DFT), and correlation methods. It discusses how semi-empirical methods approximate integrals to speed up calculations compared to Hartree-Fock. DFT is described as an alternative to wavefunction methods that uses the electron density. Popular DFT functionals and how they include exchange and correlation are outlined. Geometry optimization and vibrational frequency calculations are also summarized.
CHAPTER 10 Molecules and Solids
10.1 Molecular Bonding and Spectra
10.2 Stimulated Emission and Lasers
10.3 Structural Properties of Solids
10.4 Thermal and Magnetic Properties of Solids
10.5 Superconductivity
10.6 Applications of Superconductivity
3.1 Discovery of the X Ray and the Electron
3.2 Determination of Electron Charge
3.3 Line Spectra
3.4 Quantization
3.5 Blackbody Radiation
3.6 Photoelectric Effect
3.7 X-Ray Production
3.8 Compton Effect
3.9 Pair Production and Annihilation
Notes for Atoms Molecules and Nuclei - Part IIIEdnexa
- The document provides information about various topics in nuclear physics including de Broglie wavelength, composition and size of nucleus, isotopes, nuclear binding energy, radioactive decay, and nuclear fission.
- It defines key terms like isotopes, isobars, isotones, mass defect, nuclear binding energy, radioactive decay, half-life, decay constant, and describes the properties and characteristics of alpha particles, beta particles, and gamma rays.
- Mathematical relationships are given for radius of nucleus, mass defect, nuclear binding energy, radioactive decay law, and calculating half-life from the decay constant. Examples are provided to illustrate various concepts.
1. Quantum mechanics began with Max Planck's paper in 1900 explaining black body radiation. It extends physics to small dimensions and includes classical laws as special cases.
2. Photoelectric effect shows that light behaves as particles called photons. Einstein's equation explained it using the photon energy.
3. Compton scattering showed that photons can collide with and transfer energy to electrons. The Compton wavelength was derived from this.
The document discusses the development of quantum electrodynamics (QED) from its origins in Dirac's 1927 paper on the quantum theory of radiation. It provides an overview of the key topics covered in the subsequent chapters, including particles and fields, quantization of the electromagnetic field, Feynman diagrams, and renormalization in QED. The goal is to show how electrons and photons interact using quantum field theory by representing particles as excitations of underlying fields and developing perturbative techniques to calculate processes like scattering and radiation.
The document summarizes key details about the hydrogen atom and its electron orbital structure based on quantum mechanics. It provides:
1) A direct observation of the electron orbital of a hydrogen atom placed in an electric field, obtained through photoionization microscopy. Interference patterns observed directly reflect the nodal structure of the wavefunction.
2) Calculated and measured probability patterns for the electron in different energy levels of the hydrogen atom are shown. Bright regions correspond to high probability of finding the electron.
3) An overview of solving the radial, angular and azimuthal coordinate functions of the hydrogen atom through series expansion, as exact solutions have not been found. Approximate solutions can be obtained for more complex atoms like he
4.1 The Atomic Models of Thomson and Rutherford
4.2 Rutherford Scattering
4.3 The Classic Atomic Model
4.4 The Bohr Model of the Hydrogen Atom
4.5 Successes and Failures of the Bohr Model
4.6 Characteristic X-Ray Spectra and Atomic Number
4.7 Atomic Excitation by Electrons
Quantum mechanics provides a mathematical description of the wave-particle duality of matter and energy at small atomic and subatomic scales. It differs significantly from classical mechanics, as phenomena such as superconductivity cannot be explained using classical mechanics alone. Key aspects of quantum mechanics include wave-particle duality, the uncertainty principle, and discrete energy levels determined by Planck's constant and frequency.
The document discusses Quantum Electrodynamics and the interaction of light and matter. It explains key concepts like the Schrodinger equation, quantized energy levels, the Heisenberg Uncertainty Principle, Feynman diagrams, and the spontaneous creation and destruction of particles. While some aspects of quantum mechanics seem strange, the theories have been shown to be over 99.9999975% accurate in describing phenomena.
This document provides an overview of quantum mechanics concepts related to light and atomic structure. It discusses how light behaves as both a wave and particle, and introduces the electromagnetic spectrum. It then covers atomic structure concepts like electron configurations, energy levels, quantum numbers, and orbital shapes and filling diagrams. The document aims to explain how electrons are arranged in atoms and the underlying quantum mechanical principles.
Introduction to quantum mechanics and schrodinger equationGaurav Singh Gusain
Classical mechanics describes macroscopic objects while quantum mechanics describes microscopic objects due to limitations of classical theory. Quantum mechanics was introduced after classical mechanics failed to explain experimental observations involving microscopic particles. Some key aspects of quantum mechanics are the photoelectric effect, blackbody radiation, Compton effect, wave-particle duality, the Heisenberg uncertainty principle, and Schrodinger's wave equation. Schrodinger's equation describes the wave function and probability of finding a particle.
The document summarizes key concepts about the hydrogen atom from quantum mechanics. It begins by introducing the Schrödinger equation and how it can be applied and solved for the hydrogen atom potential. The solution involves separation of variables into radial, angular, and azimuthal components. This leads to the identification of three quantum numbers - principal (n), angular momentum (l), and magnetic (ml) - that characterize the possible energy states. Higher sections discuss properties like orbital shapes, spin, and transition selection rules between energy levels and electron probability distributions.
Quantum theory provides a framework to understand phenomena at the atomic scale that cannot be explained by classical physics. It proposes that energy is emitted and absorbed in discrete units called quanta. This explains observations like the photoelectric effect where electrons are only ejected above a threshold frequency. Light behaves as both a wave and particle - a photon. Similarly, matter exhibits wave-particle duality as demonstrated by electron diffraction. At the quantum level, only probabilities, not definite values, can be predicted. Quantum mechanics is applied to describe atomic structure and spectra.
Tyrrie Campbell is an experienced IT technician with over 10 years of experience in areas such as installation, networking, repairing, and supporting various systems. He has various technical certifications including A+, Net+, MCP, and ITIL training. He has worked in roles such as an IT instructor, HP engineer supporting blade systems and servers, service desk analyst, and technical support specialist for several companies. Campbell aims to utilize his extensive skills and experience to provide effective IT support.
This document summarizes outcomes from 100 fetal myelomeningocele (fMMC) repair procedures performed at the Children's Hospital of Philadelphia between 2011-2014. Key findings include:
- 29% of women evaluated were candidates for fMMC repair. The average gestational age at surgery was 23.4 weeks.
- Complications included membrane separation (23%), preterm premature rupture of membranes (32%), and preterm labor (38%).
- The average gestational age at delivery was 34.3 weeks. The perinatal loss rate was 6%, including 2 fetal demises and 4 neonatal deaths.
- 90.8% of women delivered at the hospital. 71% of neonates showed no
The document summarizes the individual's extensive backpacking, mountaineering, rock climbing, and outdoor leadership experience over several years. It includes over 50 backpacking trips in locations like the North Cascades, Olympic Peninsula, and Nepal. Mountaineering experience includes climbs up peaks in the North Cascades and Himalayas up to 20,187 feet. Over 100 rock climbs are listed in locations like Washington, California, Nevada, and Thailand ranging from 5.5 to 5.10d difficulty. Outdoor leadership roles are also noted.
This document outlines training materials for AT&T's Digital Life field sales experience program. It includes 9 lessons on various aspects of conducting a Digital Life field sales visit, from introducing yourself to the customer and conducting a site survey, to presenting solutions, gaining agreement and closing the sale. It provides guidance on key behaviors for the sales experience, outlines meeting agendas and sales processes, and includes training posters and templates. The document emphasizes preparing for customer visits both mentally and physically, focusing on the customer's needs, and maintaining a professional, solution-oriented approach.
This document summarizes the outcomes of 100 fetal myelomeningocele (fMMC) repair procedures performed at the Children's Hospital of Philadelphia after the Management of Myelomeningocele Study (MOMS) trial. Key findings include:
- 29% of women evaluated met criteria for fMMC repair, with an average gestational age at surgery of 23.4 weeks. Complications included membrane separation (23%), preterm premature rupture of membranes (32%), and preterm labor (38%).
- The average gestational age at delivery was 34.3 weeks. The perinatal loss rate was 6%, including 2 fetal demises and 4 neonatal deaths. Hindbrain herniation was reversed in
Lucien van Vegten has over 20 years of experience as a welder and fabricator, specializing in 6G coded welding for the oil and gas industry. He has worked for companies in the Netherlands and Scotland building structures, frames, and vessels. He also has experience in security work, serving as an Assistant Chief Security Officer and conducting surveillance. Van Vegten holds welding certifications and codes in the Netherlands and seeks to employ his skills and leadership experience as part of a dynamic team.
This document discusses Jennifer Houser's work modeling voltage-gated ion channels, spiking neurons, delay differential equations, and integrate-and-fire models. It provides an overview of these topics and describes Houser's goals of developing a mathematical model to represent feed-forward inhibition circuits and incorporating latency. Specifically, it discusses modeling ion channel gating variables, the Izhikevich spiking neuron model, delayed differential equations requiring initial values, extensions of the leaky integrate-and-fire model, and Houser's short and long-term goals of further investigating mechanisms and writing a paper.
This document provides information about Team Auto Architects' design of an ATV for the Baja SAE India 2013 competition. It summarizes the team composition, management structure, and technical areas. Key technical specifications of the designed ATV are presented, including performance targets, dimensions, suspension design, and innovations to reduce emissions. Finite element analysis was conducted on the roll cage design. Experimental stress analysis using strain gauges validated the FEA results. The project plan outlines conceptual, development, and implementation phases.
1. The document describes measuring the angle θ between momentum vectors of particles π- and Σ- produced in a particle interaction using a bubble chamber photograph. The angle can be determined by drawing tangents to the particle tracks and measuring the angle between them.
2. An alternative method to measure the angle not requiring a protractor is described using ratios of distances along the tangents.
3. Instructions are given to estimate uncertainties in measurements taken from repeated readings using calculations of average and standard deviation.
This document provides an introduction to lasers and their applications. It begins with recommended textbooks on the subject, then provides a chart showing the laser spectrum and examples of different laser types and their wavelengths. The remainder of the document discusses the basic components and functioning of lasers, including the gain medium that provides stimulated emission, the pump source to create population inversion, and the optical cavity formed by mirrors. It also provides brief histories of the development of masers and the first ruby laser.
This document provides an introduction to lasers and their applications. It begins with recommended textbooks on the subject, then provides a chart showing the laser spectrum and examples of different laser types and their wavelengths. The remainder of the document discusses the basic components and functioning of lasers, including the gain medium that provides stimulated emission, the pump source to create population inversion, and the optical cavity formed by mirrors. It also provides brief histories of the development of masers and the first ruby laser.
Quantization of photonic energy and photonic wave lengthEran Sinbar
The document proposes that if space is quantized at the Planck length, then photonic energy and wavelength must also be quantized. It suggests that future experiments could detect these quantization levels in cosmic radiation or particle collisions. It also puts forward a "grid dimensions" theory that proposes extra non-local dimensions between Planck length pieces of space that could explain quantum non-local effects like entanglement. Key equations presented quantify proposed quantized limits for momentum, mass, velocity of particles if space-time is quantized.
Von Neumann worked on the cellular automata in in late 1940’s and 1950's as an abstraction of self replication. Von Neumann's ideas of propagation of information from parent cells to next cycles in a cellular automaton, could be an explanation of the geometry of space-time grid, limitation on the speed of light, Heisenberg’s Uncertainty principle, principles of Quantum theory, Relativity, elementary particles of physics, why universe is expanding,… and the list goes on. If this simple mechanism could explain so many things, why was it not a prominent field of research? The answer is very simple but at the same time quite unexpected: one of the applications of this post war study of Von Neumann on Cellular Automata was cryptography; therefore his results were classified and still kept as top secret by USA government. However it’s time to look at this subject from a different point of view: Can this mechanism be used to explain the physical universe? we are more interested in the secret of existence than encryption-decryption of text or data; where did all these galaxies, stars, cosmological objects come from, when did it start, what it was like at the beginning of time and space
In search of multipath interference using large moleculesGabriel O'Brien
This document summarizes an experiment that tested the quantum mechanical principle of superposition using large dye molecules. The experiment measured interference patterns when the molecules passed through single, double, and triple slits. It observed less than 1% deviation from the expected interference patterns based on quantum mechanics, providing evidence that the superposition principle applies even to massive particles like these large molecules. The experiment is one of the first to directly observe quantum interference using massive particles rather than light or single particles.
Dynamic light scattering can be used to measure the diffusion of small particles undergoing Brownian motion. An experiment is described that uses a laser, sample cell containing diffusing particles, lenses, photodetector, and photon correlator. The photodetector records the scattered light as pulses, which are clustered for moving particles due to the Doppler effect. The photon correlator measures the intensity correlation function over time to determine the decay time of fluctuations, which relates to particle size and diffusion coefficient according to equations presented. Dynamic light scattering is a powerful technique for studying phenomena involving fluctuations at the microscopic scale.
This document provides a brief introduction and history of quantum mechanics. It discusses how quantum mechanics developed from Planck's hypothesis of quantized energy in 1900 to Schrodinger formulating the wave equation in 1926. The key developments include Einstein explaining the photoelectric effect in 1905, de Broglie proposing that particles are associated with waves in 1924, and Born correctly interpreting Schrodinger's wave as a probability amplitude in 1926.
This document summarizes Louis de Broglie's hypothesis of wave-particle duality and its applications. It discusses de Broglie's proposal that particles have wave-like properties with a wavelength given by Planck's constant divided by momentum. The photoelectric effect and Compton effect provide evidence of wave and particle behavior of light and electrons. Wave-particle duality is exploited in technologies like electron microscopy and neutron diffraction to examine structures smaller than visible light wavelengths. While useful, wave-particle duality does not fully explain quantum phenomena like the Heisenberg uncertainty principle.
MASSIVE PHOTON HYPOTHESIS OPENS DOORS TO NEW FIELDS OF RESEARCHijrap
1) A massive photon hypothesis is proposed, where the photon mass is directly calculated from kinetic gas theory to be 1.25605 x 10-39 kg.
2) This photon mass explains various experiments like light deflection near the Sun and the gravitational redshift.
3) The photon gas is found to behave as a perfect blackbody and ideal gas, with photons having 6 degrees of freedom.
4) The thermal de Broglie wavelength of this photon gas is calculated to be 1.75967 x 10-3 m, matching the wavelength of the cosmic microwave background radiation.
5) This links the CMB radiation to being continuously generated by the photon gas permeating space, rather than being a relic of
This document describes simulations of the Raman-Brillouin electronic density (RBED) for semiconductor thin films and superlattices. It introduces the RBED as an effective electronic density that describes resonant light scattering, even when many electronic states are involved. For isolated silicon layers, it uses the envelope function approximation to calculate electronic states and the RBED. It also describes using a tight-binding model as an alternative to obtain more realistic band structures. The RBED is then used to simulate Raman-Brillouin spectra and compare to experiments on silicon membranes.
Quantum jumps of light recording the birth and death of a photon in a cavityGabriel O'Brien
This document summarizes an experiment that observed quantum jumps in the photon number inside a superconducting cavity. Key points:
- Microwave photons were stored in a superconducting cavity for up to half a second and repeatedly probed by non-absorbing atoms passing through.
- An atom interferometer measured the atomic phase shift induced by the non-resonant cavity field, revealing the presence or absence of a single photon.
- Sequences of hundreds of correlated atom measurements were interrupted by sudden changes, recording the creation and destruction of individual photons over time.
- This realized a quantum non-demolition measurement of the photon number in the cavity in real time, allowing observation of its
This document discusses key concepts in quantum physics, including:
1. Planck's law resolved the ultraviolet catastrophe by quantizing electromagnetic radiation into discrete energy packets called photons. From fitting Planck's law to experimental data, Planck's constant h was derived.
2. Einstein's interpretation of the photoelectric effect explained experimental results by proposing light behaves as discrete photons with energy E=hf, rather than as a wave.
3. The Compton effect demonstrated light scattering off electrons, supported by photon momentum and verifying light has particle properties.
4. De Broglie's hypothesis established all matter has an associated wavelength, verifying particles exhibit wave-particle duality like light.
The document discusses the Compton effect, which describes the scattering of photons by charged particles like electrons. It provides the mathematical description using conservation of energy and momentum. The Compton effect leads to a shift in the wavelength of scattered photons. Practical applications of the Compton effect include Compton scatter densitometry to measure electron density, Compton scatter imaging for 3D electron density mapping, and Compton profile analysis to characterize materials.
This literature survey discusses plasma spectroscopy and its applications. Spectroscopy is used to characterize plasmas by determining properties like electron temperature and density. Spectroscopy works by analyzing the emissions from plasmas using instruments like monochromators and detectors. Collisional radiative models are then used to identify emitting species and plasma characteristics based on the emission data. The document provides background on the science of spectroscopy and plasmas. It also discusses experimental setup, techniques for analyzing low temperature plasma emissions, and applications of plasma spectroscopy in various fields.
The document summarizes key concepts in atomic structure:
- John Dalton proposed atoms as the smallest indivisible particles containing electrons, protons and neutrons.
- Rutherford's nuclear model presented atoms as mostly empty space with a dense positively charged nucleus.
- Bohr's model improved on this by proposing electrons orbit in fixed shells with discrete energies, explaining atomic spectra.
- Planck and Einstein established the particle-like nature of electromagnetic radiation as photons.
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Similar to Characteristics_of_Muon_Decay_Full (20)
1. Characteristics of Muon Decay
Samuel H. Trubey
Senior Physics Major, East Carolina University, North Carolina 27858
(Dated: May 10, 2013)
Abstract
Since it was first discovered in 1937, the muon has made huge contributions to the world of particle
physics. The muon is still experimented with, still validating theories like particle decay and special
relativity. This experiment was conducted to measure the average lifespan using a muon detector
with a scintillation light inside to start and stop a timing function at the beginning and the end of a
muon’s decay (respectively). After the data is collected and processed by the software collection
programs, we will calculate the average lifespan by taking the reciprocal of the average decay rate.
The end result was only 10% the accepted value, so an error
must be considered occurring during the setup or calculation process.
I. INTRODUCTION
In the November issue of Letters to the Editor in 1937, J.C. Street and E.C. Stevenson, two
research physicists from the research lab at Harvard University, submitted this:
New Evidence for the Existence of a Particle of Mass Intermediate Between
2. the Proton and Electron
The three-counter telescope consisting of tubes 1, 2, and 3 and a lead filter L for
removing shower particles, selects penetrating rays directed toward the cloud
chamber C which is in a magnetic field of 3500 gauss. [1]
Street and Stevenson weighed the mass of this new particle at roughly130 times the rest mass of
an electron, which was wrong. However, in the following July edition, Seth H. Neddermeyer and
Carl D. Anderson, from California Institute of Technology, stepped forward and not only said
Street and Stevenson were wrong, but that they had the correct values and more information:
Cosmic-Ray Particles of Intermediate Mass
A positively charged particle of about 240 electron-masses and 10 MeV energy
passes through the glass walls and copper cylinder of a tube-counter and emerges
with an energy of about 0.21 MeV. The magnetic field is 7900 gauss. The residual
range of the particle after it emerges from the counter is 2.9 cm. [1]
This once unknown particle was being grouped into Yukawa’s meson theory of strong nuclear
forces because it was offering considerable support and so most physicists attributed it to Yukawa’s
theoretical prediction. Unfortunately, the start of World War II interrupted and it wasn’t until
December of 1946 that a discrepancy was found within the new attribution to the meson theory.
[1]
Three Italian physicists (Conversi, Pancini and Piccioni) managed to stop a negative meson
particle in carbon. What they found, however, was that the decay probability is relatively close to
3. the capture probability by nuclei. This new particle was about to have some serious identity issues.
[1]
The first identity crisis was caused by misidentifying the cosmic ray mesotron as the meson
hypothesized by Yukawa. It was resolved by the experimental discovery of two distinct particles
µ and π. The second identity crisis was created by the misconception that µ and τ had to be two
different particles. It was resolved by the breakthrough of parity non-conservation, which revealed
that these two were in reality simply the different decay modes of the same particle, the kaon. [1]
The quick discovery and slow purifying process of the muon theories helped open doors to
particle physics, and has been experimented on since its unearthing nearly 80 years ago. Since then,
however, the properties of the muon have very well defined.
The muon is a negatively charged elementary particle in the lepton family, sharing the same
charge and spin as an electron, but is roughly 207 times the electron’s weight. Comprising a large
portion of cosmic rays, which collide with the earth, they decay from pions but manages to make
it to the earths surface due to its weak interaction with matter. A muons has a mean life of roughly
2.2 µs before it decays into an electron/positron, neutrino, and antineutrino, which can easily be
illustrated as such:
µ!
"e!
+!µ+!e or µ+
!e+
+!µ+!µ.[2][3]
For this experiment, the mean lifetime of the muon will be quantized with the given ability to
measure the average time of decay at sea level from our own personal detector. The primary bulk
of the detector is a 15 cm wide and 12.5 cm tall cylindrical plastic scintillator beneath a black
anodized aluminum alloy tube. The scintillator is made from a transparent organic compound
mixture and as a charged particle passes through, it will lose some of its kinetic energy by
ionization and atomic excitation of the solvent molecules. [4] As high energy muons pass through
4. the scintillator, some of its kinetic energy is stripped and excites the electrons of the scintillator,
causing a photon emission. This emission then triggers a reactive process, initiating the detectors
system to begin timing and cease timing when the muon eventually breaks down and emits an
electron. It is that small frame of time where the lifetime of a muon is measured.
It is important to note that there is both a positive and negative muon (hence the two diagrams
above) and furthermore, the negative muon’s lifetime is slightly less due to its weaker interaction
with the protons of the scintillator; this is why we are measuring the mean lifetime. How do we
find the mean? Well, in a simpler setting, the situation could be expressed as a simple exponential
relation of radioactive decay:
N(t)= N0exp(!!t) , (1)
where N is the number of remaining muons after time t and N0 is the original amount of muons at
t=0. λ is the decay rate of the given particle, and τ is the lifetime of the particle, being the reciprocal
of the decay rate, 1/λ. [4] The lifetime, τ, of the muons is given by the computer muon detection
program after the collection phase has been completed, the ideal value being τµ = 2.19703 ±
0.00004 µsec. It if from this provided value that we can easily calculate the decay rate and time
distribution seen below. [4]
This friendly looking equation is, unfortunately, impractical in this situation because we do not
have a single cluster of surviving muons we can easily count, nor do they come in clumps in the
first place. Decay time distribution D(t), will allow us to notate the time-dependent probability that
a muon decays in the time interval between t and t + dt as a given function D(t)dt. So in the off
chance we did know the starting number of muons, the fraction −dN/N0 would show the average
decay amount in the time interval between t and t + dt. This is just a derivation from the relation
above:
5. −dN = N0 λ(−λ t)
dt (2)
−dN/ N0 = λ(−λ t)
dt. (3)
The first part of Eq. (3) has nothing else but the decay probability, which we are seeking! The
decay rate as a function of time can be expressed as the exponential function,
D(t) = λe(−λ t)
. (4)
This works because N0 is irrelevant here because D(t) would be true, regardless of the original
number of particles. This is true because the distribution of decay times, for newer muons entering
the detector, uses the same exponential power to describe the number of surviving muons.
Reminder, we express muon lifetime as
τ= 1/ λ. [4] (5)
II. METHODS
To begin to talk about methods, I must first mention the technical difficulty that my partner,
Wilson Hawkins, and I encountered during our data collection phase. Happening twice, I initiated
and ran the software to begin detecting muon decays and I allowed it to continue collecting data
for several days. When I returned five days later, however, the computer was powered off, having
most likely been rebooted at some point over the weekend. I would attempt to run the program
again, planning on returning the following day to analyze data collected over 24 hours but I
encountered a similar problem yet again. The computer was non-responsive for several minutes,
6. and once it began to function normally again, it was apparent that the default user account was
logged off and upon reentry, all software had already shutdown so all data collections were lost.
After consulting with my professor and lab advisor, a decision to abandon the procedure of running
the equipment was made and my partner and I were to just use data from previous, successful trials
to analyze.
With this being said, the data collection stage consisted of both hardware and software. A muon
detector was connected to a Teach Spin muon physics electronics box which was the subsequently
connected to a computer which piloted the Teach Spin data collecting software which controlled
and monitored the detector.
Inside the detector was a perpetual chain reaction. Within the muon detector was a scintillation
light, which is detected by a photomultiplier tube (PMT), which then outputs a signal fed into a
two-stage amplifier. The amplifier output supplies an adjustable threshold to a voltage
discriminator where a transistor-transistor logic (TTL) pulse is created. This produced TTL pulse
is for input signals that are above the threshold so the pulse can activate the timing circuit for the
field-programmable gate array (FPGA). Within a certain time interval, a second TTL output pulse
is sent to the FPGA input, stopping and resetting the timing circuit (the duration of this reset last
roughly 1.0 x10-3
seconds). It is not the pulses, but the time between the pulses that is important
for this experiment; the interval’s data is passed through a communications module where the
lifetime of the muon is calculated before reaching the computer (Figure 1). [4]
The extent of actual work done to set up and run the calculations was minimal. There were only
three parts to tend to and make sure they were already connected in the proper sequential order;
after confirming that the detector and the electronics box were connected by the power source and
signal cable, the electronics box was connected to the computer, we were ready to begin. The
7. electronics box was powered on and then the high voltage supply was set to 1200 Volts and the
discriminator was set to 200 mV while the “Time Adj” and the “HV Adj” dials on the muon
detector were set to ten. Once that was completed, we were ready for software operation.
The first thing that needed to be done was to configure the program “muon”, found in the
“muon_data” folder. Underneath the “Control” icon is the “configure” icon, resulting in a new
menu, as seen in Figure 2. It is here that port “com1”, a time scale of 20 microseconds for the decay
histogram, and bin number 60 were respectively selected to finalize configuration. Once this was
done, the final step is to click “Start” and allow the program to function and collect the detections
and decay rates. The judgment and determination of the event was performed completely by the
software, operating just as I have described earlier. But to delve in a little further now, the TTL
pulses, which start and stop the time detecting intervals, are triggered when a detected muon begins
to slow. As a muon begins to slow and decay, it will ultimately break down into three lesser
particles, an electron, a neutrino, and an antineutrino. The excited electron has enough energy to
surmount the threshold and trigger the scintillator, releasing another burst of light to generate the
closing TTL pulse. Once the program is finished, it consolidates all the data collected and a
histogram chart that displays the total events and the muon decay rate, the reciprocal will be take
to satisfy Eq. (5) and that will consequently provide us with the measured lifespan. [4]
III. RESULTS
Table 1 displays our final results, after the calculations of decay probability and half-life. First,
the half-life was determined with Eq. 5 by simply finding the reciprocal of the muon’s provided
lifetime value, τ=4.568±2.03µs.
8. Uncertainty is being taken into account with the propagation of an uncertainty with a power, we
use:
!q= n!x , (6)
q x
where n is -1. Half-life λ=0.219±0.097µs. With the half-life determined, the time distribution can
be calculated using Eq. 4. Once more, the uncertainty must be determined so we begin with the
distribution equation, D(t) = λe(−λ t)
. The uncertainty of the product of decay rate and exponential
distribution, the exponent, and the product within the exponent must be determined. For
demonstration, we will assign an arbitrary variable b to the exponent. For this calculation, we will
also assume that the elapse time, t, is a constant 72 hours (2.592×10!!µμs). The uncertainty of the
exponent can be determined as
!b =t!!", (7)
where != !" (5.676×10!"!").
!b =t!!"
!b = 2.592!1011
µs!0.097 !b =
2.514!1010
µs.
Now that the uncertainty of the exponent has been determined, Eq. 6 can be translated as the
propagation of uncertainty of a product, being:
2 2 (8)
!D =e! "$!b%' +"!"% ,
$ '
D # b & # "&
9. where D(t) = λe(−λ t) (0.219×!!.!"!×!"!").
"!b%2
"!"%2
!D
= e! $ ' +$ '
D # b & # "&
!D "2.514!1010
%2
"0.097%2
= e! $ 10 ' +$ '
D #5.676!10 & #0.219&
!D
= e! 0.392 D
!D
= 0.626e
D 1.135!1011
!D= 0.137!e
So the decay time distribution is calculated at 0.219×e5.676×1010 ±0.137×e1.135×1011.
IV. DISCUSSION
Our calculated decay rate is an order of power smaller than the accepted value of the average
muon decay rate. Since the detection and calculations were done by the scintillator and the lifetime
of the muon was determined by the Teach Spin software, respectively, there was hardly any room
for human error. It is possible, however, that the source of possible human error generated from
the calibration of the electronics in the beginning before the detection process even began.
Another possible source, which would cause our value to deviate from the accepted value, was
inclement weather. The weather during the 72-hour elapse time was plagued with clouds and rain.
This could have possibly skewed the amount of muons reached our detector, though I'm not sure
10. to what extent the weather would affect the muons travel when the muon travels at such high
speeds.
Given the chance to possibly run the program again and compare data between research groups,
it is more than likely that a more acceptable value would be derived, given the correct parameters
were met during the conveyance of the experiment.
V. CONCLUSION
Our value of the decay rate of the muons reach our altitude was significantly smaller than the
accepted value, so a catastrophic error must be assumed and the data collection process must be
reevaluated and possibly conducted again. I believe that the final result neither proves nor negates
the theoretical value, but rather shows there was an error present during the experiment that
generated the large divergence.
VI. ACKNOWLEDGEMENTS
I’d like to thank my colleagues and fellow classmates Sarim Akbar and Maneesh
Jeyakumar for sharing their data with me when I was unable to calculate the raw numbers
without the proper computer functions.
VII. REFERENCES
[1] Lee, T. D. December 01, 1994. A brief history of the muon. Hyperfine interactions 86, no. 1,
(accessed May 11, 2013).
11. [2] Collins Dictionary of Astronomy, s.v. "muon," accessed May 11, 2013,
http://www.credoreference.com/entry/collinsastron/muon
[3] The Penguin Dictionary of Physics, s.v. "muon," accessed May 11, 2013,
http://www.credoreference.com/entry/pendphys/muon
[4] Department of Physics. Muon Physics. User Manual, Southern Methodist University, Dallas,
Texas: Department of Physics.
TABLE 1. Final calculated results for decay rate and the time distribution of the decay rate of a
muon from the measured values detected during the experiment.
Collection Elapse Time, t (hours) 72
Total Muons 153428
Total events 959
Average Lifetime, τ (µseconds) 4.568±2.03
Decay Rate, λ (µseconds) 0.219±0.097
Decay Time Distribution, D(t) 0.219×e!.!"!×!"!" ±0.137×e!.!"#×!"!!
12. FIGURE 1. The schematic of the detector and electronics box setup, most of which is consisted
within the detector, itself. This displays the process of detection and information processing before
it is sent to the computer for analyzation. [4]
FIGURE 2. A sample screen capture during the calibration process before the detector is started
and the muon decays are measured. [4]