The Schrodinger equation plays the role of Newton's laws and conservation of energy in classical mechanics by predicting the future behavior of dynamic systems. It is a wave equation that uses the wavefunction to analytically and precisely predict the probability of events or outcomes, though not the strict determination of a detailed outcome. The kinetic and potential energies are transformed into the Hamiltonian which acts on the wavefunction to generate its evolution in time and space, giving the quantized energies of the system and the form of the wavefunction to calculate other properties.
These slides are especially made to understand the postulates of quantum mechanics or chemistry better. easily simplified and at one place you will find each of relevant details about the 5 postulates. so go through it & trust me it will help you a lot if you are chemistry or a science student.
well done
Dielectrics are materials that have permanent electric dipole moments. All dielectrics are electrical insulators and are mainly used to store electrical energy by utilizing bound electric charges and dipoles within their molecular structure. Important properties of dielectrics include their electric intensity or field strength, electric flux density, dielectric parameters such as dielectric constant and electric dipole moment, and polarization processes including electronic, ionic, and orientation polarization. Dielectrics are characterized by their complex permittivity, which relates to their ability to transmit electric fields and is dependent on factors like frequency, temperature, and humidity that can influence dielectric losses.
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.
this slide is introduce the postulates of quantum mechanics in which has all important definable objects is defined. so that presentation is helpful for the undergraduate students
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.
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.
The presentation opens up by introducing Schrodinger's time dependent and independent wave equation. Then it covers the derivation of time independent wave equation, followed by its applications.
The Schrodinger equation plays the role of Newton's laws and conservation of energy in classical mechanics by predicting the future behavior of dynamic systems. It is a wave equation that uses the wavefunction to analytically and precisely predict the probability of events or outcomes, though not the strict determination of a detailed outcome. The kinetic and potential energies are transformed into the Hamiltonian which acts on the wavefunction to generate its evolution in time and space, giving the quantized energies of the system and the form of the wavefunction to calculate other properties.
These slides are especially made to understand the postulates of quantum mechanics or chemistry better. easily simplified and at one place you will find each of relevant details about the 5 postulates. so go through it & trust me it will help you a lot if you are chemistry or a science student.
well done
Dielectrics are materials that have permanent electric dipole moments. All dielectrics are electrical insulators and are mainly used to store electrical energy by utilizing bound electric charges and dipoles within their molecular structure. Important properties of dielectrics include their electric intensity or field strength, electric flux density, dielectric parameters such as dielectric constant and electric dipole moment, and polarization processes including electronic, ionic, and orientation polarization. Dielectrics are characterized by their complex permittivity, which relates to their ability to transmit electric fields and is dependent on factors like frequency, temperature, and humidity that can influence dielectric losses.
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.
this slide is introduce the postulates of quantum mechanics in which has all important definable objects is defined. so that presentation is helpful for the undergraduate students
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.
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.
The presentation opens up by introducing Schrodinger's time dependent and independent wave equation. Then it covers the derivation of time independent wave equation, followed by its applications.
This document provides an introduction to quantum mechanics concepts including:
1. It describes Schrodinger's wave equation and its applications, including quantized energy levels and tunneling effects.
2. Wave-particle duality is discussed through experiments demonstrating the wave-like and particle-like properties of electrons.
3. The uncertainty principle and solutions to Schrodinger's wave equation for simple potential wells are presented, showing energy levels are quantized.
This document discusses statistical mechanics and the distribution of energy among particles in a system. It provides 3 main types of statistical distributions based on the properties of identical particles: Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics. Maxwell-Boltzmann statistics applies to distinguishable particles, while Bose-Einstein and Fermi-Dirac apply to indistinguishable particles (bosons and fermions respectively), with the key difference being that fermions obey the Pauli exclusion principle. The document also discusses applications of these distributions, including the Maxwell-Boltzmann distribution law for molecular energies in an ideal gas.
1. The document discusses key concepts in quantum physics including Planck's quantum theory, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's time-independent wave equation.
2. It provides details on experiments that verified the wave-like properties of matter including electron diffraction experiments by Davisson and Germer.
3. The document derives expressions for the energy levels of particles confined in one-dimensional potential wells and boxes in terms of Planck's constant and other variables.
Russell Saunders coupling and J-J coupling describe different schemes for coupling angular momenta in atomic systems. Russell Saunders coupling occurs when spin-orbit interactions are weaker than interactions between electrons. It involves combining orbital angular momenta (L) and spins (S) into total angular momentum (J). J-J coupling occurs in heavy atoms where spin-orbit interactions are strong. It involves first combining orbital and spin angular momenta for individual electrons (j) and then combining the j values. The document also discusses the anomalous Zeeman effect, Paschen-Back effect, and applications of the Fabry-Perot interferometer for measuring Zeeman splitting.
This document provides an overview of statistical mechanics. It defines microstates and macrostates, and explains that statistical mechanics studies systems with many microstates corresponding to a given macrostate. The Boltzmann distribution is derived, which gives the probability of finding a system in a particular microstate as being proportional to the exponential of the negative of the energy of that microstate divided by the temperature. Maxwell-Boltzmann statistics are described as applying to classical distinguishable particles, yielding the Maxwell-Boltzmann distribution. References for further reading are also included.
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.
Quantum mechanics is a branch of physics that deals with phenomena at microscopic scales, describing the wavelike and particle-like behavior of energy and matter. Erwin Schrödinger developed the wave equation and Schrödinger equation, which provide a mathematical description of quantum systems. Werner Heisenberg, Max Born, and Pascual Jordan created an equivalent formulation of quantum mechanics called matrix mechanics, which is the basis of Dirac's bra-ket notation for the wave function.
The document is a presentation on dielectrics that covers:
- The basic terms related to dielectrics including electric field, flux, and dielectric constant.
- The different types of polarization that can occur in dielectrics including electronic, ionic, orientation, and interfacial polarization.
- How the internal electric field is calculated for a dielectric material placed between the plates of a capacitor.
- The various types of dielectric materials including solid, liquid, and gaseous dielectrics.
- The key properties desired in a good dielectric material and examples of applications for dielectrics such as in capacitors and transformers.
Pieter Zeeman was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Hendrik Lorentz for his discovery of the Zeeman effect in 1896. The Zeeman effect is the splitting of spectral lines into multiple components when in the presence of a magnetic field. Zeeman observed that each emission line from a light source split into several lines when under the influence of a magnetic field. This splitting, known as the Zeeman effect, demonstrated that atomic energy levels are affected by magnetic fields.
Ferroelectric and piezoelectric materialsZaahir Salam
The document discusses piezoelectric and ferroelectric materials. It defines key terms like dielectric, polarization, and piezoelectric effect. It explains that piezoelectric materials can convert mechanical energy to electrical energy and vice versa. Ferroelectric materials are a special class of piezoelectric materials that exhibit spontaneous polarization without an electric field. Examples of naturally occurring and man-made piezoelectric crystals and ceramics are provided. Common applications of piezoelectric materials include sensors, actuators, generators, and memory devices.
1) Identical particles are particles that can be substituted for each other without changing the physical situation. The particle exchange operator P12 interchanges the coordinates of particles 1 and 2 and commutes with the Hamiltonian.
2) The eigenstates of the particle exchange operator P12 have eigenvalues of +1 or -1, corresponding to symmetric and antisymmetric wave functions respectively.
3) Pauli's principle states that systems of identical particles with half-integer spin obey Fermi-Dirac statistics and have antisymmetric wave functions, while those with integer spin obey Bose-Einstein statistics and have symmetric wave functions.
1. Quantum mechanics describes the behavior of matter and light at the atomic scale, which is very different from classical mechanics. Particles have both wave-like and particle-like properties.
2. The de Broglie hypothesis proposed that all particles have an associated wavelength that depends on their momentum. This was confirmed experimentally by observing electron diffraction patterns.
3. Heisenberg's uncertainty principle states that it is impossible to precisely measure both a particle's position and momentum simultaneously. This limits our ability to predict the future behavior of particles.
This document provides an overview of quantum mechanics. It begins by explaining that quantum mechanics describes the motion of subatomic particles and is needed to understand the properties of atoms and molecules. It then discusses some key developments in quantum mechanics, including Planck's quantum theory of radiation, Einstein's explanation of the photoelectric effect, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's wave equation. The document also compares classical and quantum mechanics and provides examples of quantum mechanical applications like atomic orbitals and black body radiation.
Introduction, measurement of uncertainty, Heisenberg microscope, challenges to Heisenberg principle, examples of Heisenberg uncertainty principle, applications of uncertainty principle
Nuclear Quadrupole Resonance Spectroscopy (NQR) is a chemical analysis technique that detects nuclear energy level transitions in the absence of a magnetic field through the absorption of radio frequency radiation. NQR is applicable to solids due to the quadrupole moment averaging to zero in liquids and gases. The interaction between a nucleus's quadrupole moment and the electric field gradient of its surroundings results in quantized energy levels. Transitions between these levels are detected as NQR spectra and provide information about electronic structure, hybridization, and charge distribution. NQR finds applications in studying charge transfer complexes, detecting crystal imperfections, and locating land mines.
This document provides an introduction to statistical mechanics and different types of statistics. It discusses classical statistics, which includes Maxwell-Boltzmann statistics, and quantum statistics, which includes Bose-Einstein (B-E) and Fermi-Dirac (F-D) statistics. Maxwell-Boltzmann statistics treats particles as distinguishable and applies to ideal gases, while B-E and F-D statistics treat particles as indistinguishable and apply to photons/bosons and electrons/fermions, respectively. The key differences between the statistics are whether particles can occupy the same state (B-E allows multiple occupancy, F-D allows only single occupancy) and the formulas that describe the most probable distribution of particles
This is a schrodinger equation and also Heiseinberg's uncertainty principle.
It is necessary to know this equation for the quantum mechanic. The wave equation, uncertainty principle of Heisenberg, time dependent and independent of schrodinguer...
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.
This document provides an introduction to quantum mechanics concepts including:
1. It describes Schrodinger's wave equation and its applications, including quantized energy levels and tunneling effects.
2. Wave-particle duality is discussed through experiments demonstrating the wave-like and particle-like properties of electrons.
3. The uncertainty principle and solutions to Schrodinger's wave equation for simple potential wells are presented, showing energy levels are quantized.
This document discusses statistical mechanics and the distribution of energy among particles in a system. It provides 3 main types of statistical distributions based on the properties of identical particles: Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics. Maxwell-Boltzmann statistics applies to distinguishable particles, while Bose-Einstein and Fermi-Dirac apply to indistinguishable particles (bosons and fermions respectively), with the key difference being that fermions obey the Pauli exclusion principle. The document also discusses applications of these distributions, including the Maxwell-Boltzmann distribution law for molecular energies in an ideal gas.
1. The document discusses key concepts in quantum physics including Planck's quantum theory, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's time-independent wave equation.
2. It provides details on experiments that verified the wave-like properties of matter including electron diffraction experiments by Davisson and Germer.
3. The document derives expressions for the energy levels of particles confined in one-dimensional potential wells and boxes in terms of Planck's constant and other variables.
Russell Saunders coupling and J-J coupling describe different schemes for coupling angular momenta in atomic systems. Russell Saunders coupling occurs when spin-orbit interactions are weaker than interactions between electrons. It involves combining orbital angular momenta (L) and spins (S) into total angular momentum (J). J-J coupling occurs in heavy atoms where spin-orbit interactions are strong. It involves first combining orbital and spin angular momenta for individual electrons (j) and then combining the j values. The document also discusses the anomalous Zeeman effect, Paschen-Back effect, and applications of the Fabry-Perot interferometer for measuring Zeeman splitting.
This document provides an overview of statistical mechanics. It defines microstates and macrostates, and explains that statistical mechanics studies systems with many microstates corresponding to a given macrostate. The Boltzmann distribution is derived, which gives the probability of finding a system in a particular microstate as being proportional to the exponential of the negative of the energy of that microstate divided by the temperature. Maxwell-Boltzmann statistics are described as applying to classical distinguishable particles, yielding the Maxwell-Boltzmann distribution. References for further reading are also included.
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.
Quantum mechanics is a branch of physics that deals with phenomena at microscopic scales, describing the wavelike and particle-like behavior of energy and matter. Erwin Schrödinger developed the wave equation and Schrödinger equation, which provide a mathematical description of quantum systems. Werner Heisenberg, Max Born, and Pascual Jordan created an equivalent formulation of quantum mechanics called matrix mechanics, which is the basis of Dirac's bra-ket notation for the wave function.
The document is a presentation on dielectrics that covers:
- The basic terms related to dielectrics including electric field, flux, and dielectric constant.
- The different types of polarization that can occur in dielectrics including electronic, ionic, orientation, and interfacial polarization.
- How the internal electric field is calculated for a dielectric material placed between the plates of a capacitor.
- The various types of dielectric materials including solid, liquid, and gaseous dielectrics.
- The key properties desired in a good dielectric material and examples of applications for dielectrics such as in capacitors and transformers.
Pieter Zeeman was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Hendrik Lorentz for his discovery of the Zeeman effect in 1896. The Zeeman effect is the splitting of spectral lines into multiple components when in the presence of a magnetic field. Zeeman observed that each emission line from a light source split into several lines when under the influence of a magnetic field. This splitting, known as the Zeeman effect, demonstrated that atomic energy levels are affected by magnetic fields.
Ferroelectric and piezoelectric materialsZaahir Salam
The document discusses piezoelectric and ferroelectric materials. It defines key terms like dielectric, polarization, and piezoelectric effect. It explains that piezoelectric materials can convert mechanical energy to electrical energy and vice versa. Ferroelectric materials are a special class of piezoelectric materials that exhibit spontaneous polarization without an electric field. Examples of naturally occurring and man-made piezoelectric crystals and ceramics are provided. Common applications of piezoelectric materials include sensors, actuators, generators, and memory devices.
1) Identical particles are particles that can be substituted for each other without changing the physical situation. The particle exchange operator P12 interchanges the coordinates of particles 1 and 2 and commutes with the Hamiltonian.
2) The eigenstates of the particle exchange operator P12 have eigenvalues of +1 or -1, corresponding to symmetric and antisymmetric wave functions respectively.
3) Pauli's principle states that systems of identical particles with half-integer spin obey Fermi-Dirac statistics and have antisymmetric wave functions, while those with integer spin obey Bose-Einstein statistics and have symmetric wave functions.
1. Quantum mechanics describes the behavior of matter and light at the atomic scale, which is very different from classical mechanics. Particles have both wave-like and particle-like properties.
2. The de Broglie hypothesis proposed that all particles have an associated wavelength that depends on their momentum. This was confirmed experimentally by observing electron diffraction patterns.
3. Heisenberg's uncertainty principle states that it is impossible to precisely measure both a particle's position and momentum simultaneously. This limits our ability to predict the future behavior of particles.
This document provides an overview of quantum mechanics. It begins by explaining that quantum mechanics describes the motion of subatomic particles and is needed to understand the properties of atoms and molecules. It then discusses some key developments in quantum mechanics, including Planck's quantum theory of radiation, Einstein's explanation of the photoelectric effect, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's wave equation. The document also compares classical and quantum mechanics and provides examples of quantum mechanical applications like atomic orbitals and black body radiation.
Introduction, measurement of uncertainty, Heisenberg microscope, challenges to Heisenberg principle, examples of Heisenberg uncertainty principle, applications of uncertainty principle
Nuclear Quadrupole Resonance Spectroscopy (NQR) is a chemical analysis technique that detects nuclear energy level transitions in the absence of a magnetic field through the absorption of radio frequency radiation. NQR is applicable to solids due to the quadrupole moment averaging to zero in liquids and gases. The interaction between a nucleus's quadrupole moment and the electric field gradient of its surroundings results in quantized energy levels. Transitions between these levels are detected as NQR spectra and provide information about electronic structure, hybridization, and charge distribution. NQR finds applications in studying charge transfer complexes, detecting crystal imperfections, and locating land mines.
This document provides an introduction to statistical mechanics and different types of statistics. It discusses classical statistics, which includes Maxwell-Boltzmann statistics, and quantum statistics, which includes Bose-Einstein (B-E) and Fermi-Dirac (F-D) statistics. Maxwell-Boltzmann statistics treats particles as distinguishable and applies to ideal gases, while B-E and F-D statistics treat particles as indistinguishable and apply to photons/bosons and electrons/fermions, respectively. The key differences between the statistics are whether particles can occupy the same state (B-E allows multiple occupancy, F-D allows only single occupancy) and the formulas that describe the most probable distribution of particles
This is a schrodinger equation and also Heiseinberg's uncertainty principle.
It is necessary to know this equation for the quantum mechanic. The wave equation, uncertainty principle of Heisenberg, time dependent and independent of schrodinguer...
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.
Beyond bohr de broglie and heisenberg for universe to atom module cfiCraig Fitzsimmons
This document summarizes the development of quantum mechanics from Bohr's early model of the atom to the fully quantum models developed in the 1920s. It discusses modifications made to Bohr's model, such as elliptical orbits and additional quantum numbers. Key figures who contributed include de Broglie, Heisenberg, Schrodinger, and Pauli. De Broglie hypothesized that particles have wave-like properties, which was confirmed by Davisson and Germer's electron diffraction experiment. Heisenberg formulated matrix mechanics and proposed the uncertainty principle. Schrodinger developed wave mechanics using wave functions, and his equation can be used to calculate energy levels.
Quantum teleportation allows the transfer of quantum states between particles at a distance without physically transporting the particles themselves. It relies on the phenomenon of quantum entanglement where the quantum states of particles become linked even when separated spatially. The experiment demonstrated successful quantum teleportation of photons' polarization states between two locations, confirming the non-local effects predicted by quantum mechanics. This technique could enable future applications for quantum communication but does not allow the teleportation of macroscopic objects as depicted in science fiction.
The document discusses the photoelectric effect, which provided evidence that light has both wave-like and particle-like properties. It describes how photons interacting with electrons in solids can eject the electrons, called the photoelectric effect. This discovery supported Max Planck's theory that energy exists in discrete units called quanta and is proportional to frequency, helping establish quantum mechanics. The document also discusses quantization of energy in atoms and molecules and how photons maintain their energy characteristics as they travel through space until interacting with an object.
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.
This document provides an overview of Module 4 which covers Quantum Mechanics and LASERs. The key topics in Quantum Mechanics include Planck's Law, wave-particle duality, de Broglie's hypothesis, Heisenberg's Uncertainty Principle, Schrodinger's wave equation, and wave functions. LASER is also introduced including spontaneous and stimulated emission, laser construction and working principles of CO2 and semiconductor lasers, and applications such as laser range finders and data storage. References for 15 books on related topics are provided.
The document provides information on quantum theory and its application to atomic structure. It discusses key concepts such as:
1) Energy is quantized and can only be emitted or absorbed in discrete packets called quanta.
2) Electrons in atoms exist in discrete energy levels called shells or orbitals. They can only transition between these levels by absorbing or emitting quanta of energy.
3) Quantum numbers are used to describe the specific energy state of each electron in an atom, including its distance from the nucleus, energy, and orientation.
The document discusses wave-particle duality and Louis de Broglie's hypothesis that all matter has both wave-like and particle-like properties. It summarizes key experiments that supported this idea, including Davisson and Germer's 1927 experiment in which electron beams were diffracted by crystal lattices, demonstrating their wave-like behavior. The document also explains how de Broglie's hypothesis resolved issues with early atomic models by introducing the concept of electron standing waves within atoms.
1. The document discusses principles of quantum chemistry including classical mechanics and its inadequacies in explaining phenomena at the atomic level, Planck's quantum theory, and properties of electromagnetic radiation.
2. Key concepts covered include de Broglie's equation describing the wave-like nature of matter, Heisenberg's uncertainty principle, explanations of photoelectric effect and blackbody radiation.
3. The document also introduces quantum numbers, Hund's rule, Pauli's exclusion principle, and Aufbau's principle, which describe allowable electron configurations in atoms and molecules.
This document discusses the history and principles of quantum mechanics. It describes how early theories of light and matter as particles or waves evolved into the modern understanding of wave-particle duality. Key concepts explained include the photoelectric effect demonstrating light behaving as quantized particles, the de Broglie hypothesis extending wave-particle duality to all matter, Heisenberg's uncertainty principle limiting the precision of simultaneous position and momentum measurements, and consequences like zero-point energy and virtual particles arising from short time fluctuations allowed by the principle.
The document discusses the wave properties of particles. Some key points:
1) Louis de Broglie hypothesized in 1924 that matter has an associated wave-like nature with a wavelength given by Planck's constant divided by momentum.
2) A particle can be represented as a localized "wave packet" resulting from the interference and superposition of multiple waves with slightly different wavelengths and frequencies.
3) Davisson and Germer's electron diffraction experiment in 1927 provided direct evidence of the wave nature of electrons and supported de Broglie's hypothesis by measuring electron wavelengths matching those expected.
This document discusses the failure of classical mechanics and the development of quantum mechanics. It provides evidence that classical concepts like particles, waves, determinism and continuity do not fully describe the atomic world. New models were proposed including de Broglie's idea that matter has wave-like properties. This was supported by experiments showing electron diffraction, demonstrating their wave nature. Ultimately, Schrodinger's quantum mechanical model was needed to fully explain atomic structure and behavior.
This document provides an introduction to quantum mechanics concepts including:
- Quantum mechanics describes nature at small scales where classical physics is insufficient. Pioneers who established the foundations of quantum mechanics are mentioned.
- Key concepts are introduced such as wave-particle duality, matter waves, Heisenberg's uncertainty principle and its application to electrons not existing in atomic nuclei.
- The Schrodinger wave equation is derived and applied to problems such as a particle in an infinite potential well to solve for energy eigenstates and eigenvalues.
The Significance of the Speed of Light relating to EinsteinKenny Hansen
This document discusses Albert Einstein's Special Theory of Relativity and how it relates to the universal constant speed of light. It explores how light can behave as both a particle and wave, and how its speed is directly linked to concepts like mass, time, and energy. The speed of light is fundamental to our understanding of physics and the nature of the universe according to Einstein's theory.
1. The document provides an overview and review of topics covered on the AP Physics B exam related to modern physics, including the photoelectric effect, Bohr model of the atom, and nuclear physics.
2. It describes Einstein's explanation of the photoelectric effect involving photons and how it resolved issues not explained by classical wave theory.
3. It also explains the Bohr model of the hydrogen atom, including Bohr's assumptions and how it leads to quantized electron orbits that can explain atomic emission spectra.
Werner Heisenberg developed the uncertainty principle, which states that the more precisely the position of a particle is determined, the less precisely its momentum can be known, and vice versa. This stems from the quantum nature of matter, where measuring devices disturb the system being measured. A thought experiment is described where observing an electron's position with a photon impacts the electron's momentum in an unpredictable way. The uncertainty principle is expressed as ΔxΔp≥h/2π, meaning the product of the uncertainties in position and momentum must be greater than or equal to Planck's constant divided by 2π.
This document provides an overview of key topics in early quantum theory that students should understand, including:
- Electrons, J.J. Thompson's experiment determining the electron, and Millikan's experiment measuring the charge of an electron.
- De Broglie's relation connecting the wavelength of a particle to its momentum.
- Wave-particle duality and the principle of complementarity established by Bohr.
- That matter can behave as waves according to de Broglie's theory of the dual nature of matter.
- Planck's quantum hypothesis that the energy of atomic oscillations is quantized in integer multiples of Planck's constant.
This document provides an overview of key topics in early quantum theory that students should understand, including:
- Electrons, J.J. Thompson's experiment determining the electron, and Millikan's experiment measuring the charge of an electron.
- De Broglie's relation connecting the wavelength of a particle to its momentum.
- Wave-particle duality and the principle of complementarity stating that particles can behave as both waves and particles.
- Planck's quantum hypothesis that the energy of atomic oscillations is quantized in integer multiples of Planck's constant.
The document provides background information on Einstein's special theory of relativity. It discusses the two postulates of special relativity: 1) the principle of relativity, and 2) the constancy of the speed of light. It then summarizes some key consequences of special relativity, including time dilation, length contraction, relativistic Doppler effect, relativistic mass, mass-energy equivalence, and Lorentz transformations. Examples are provided to demonstrate calculations for these various consequences.
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International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
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Understanding Inductive Bias in Machine LearningSUTEJAS
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Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMSIJNSA Journal
The smart irrigation system represents an innovative approach to optimize water usage in agricultural and landscaping practices. The integration of cutting-edge technologies, including sensors, actuators, and data analysis, empowers this system to provide accurate monitoring and control of irrigation processes by leveraging real-time environmental conditions. The main objective of a smart irrigation system is to optimize water efficiency, minimize expenses, and foster the adoption of sustainable water management methods. This paper conducts a systematic risk assessment by exploring the key components/assets and their functionalities in the smart irrigation system. The crucial role of sensors in gathering data on soil moisture, weather patterns, and plant well-being is emphasized in this system. These sensors enable intelligent decision-making in irrigation scheduling and water distribution, leading to enhanced water efficiency and sustainable water management practices. Actuators enable automated control of irrigation devices, ensuring precise and targeted water delivery to plants. Additionally, the paper addresses the potential threat and vulnerabilities associated with smart irrigation systems. It discusses limitations of the system, such as power constraints and computational capabilities, and calculates the potential security risks. The paper suggests possible risk treatment methods for effective secure system operation. In conclusion, the paper emphasizes the significant benefits of implementing smart irrigation systems, including improved water conservation, increased crop yield, and reduced environmental impact. Additionally, based on the security analysis conducted, the paper recommends the implementation of countermeasures and security approaches to address vulnerabilities and ensure the integrity and reliability of the system. By incorporating these measures, smart irrigation technology can revolutionize water management practices in agriculture, promoting sustainability, resource efficiency, and safeguarding against potential security threats.
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMS
Review of Elementary Quantum Mechanics
1. Review of Elementary Quantum
Mechanics
Unit I & II
Dr Md Kaleem
Department of Applied Sciences
Jahangirabad Institute of Technology (JIT),
Jahangirabad, Barabanki(UP) - 225203
1/28/2017 1DR MD KALEEM/ ASSISTANT PROFESSOR
2. Objective
• Know the background for and the main features in the historical
development of quantum mechanics.
• Explain, qualitatively and quantitatively, the role of photons in
understanding phenomena such as the photoelectric effect
• Be able to discuss and interpret experiments displaying wavelike
behavior of matter, and how this motivates the need to replace
classical mechanics by a wave equation of motion for matter (the
Schrödinger equation).
• Understand the central concepts and principles of quantum
mechanics: the Schrödinger equation, the wave function and its
physical interpretation.
• Interpret and discuss physical phenomena in light of the uncertainty
relation.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
3. • An idealized body that absorbs all incident EM
radiation incident on it, regardless of frequency or
angle of incidence is called a black body
• Implication: 1. Zero reflection, 2. Zero transmittance
• It is true for : 1. All wavelengths, 2. All incident directions
• Corollary: A black body emits maximum amount of radiation
at a given temperature
Black Body Radiation
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
5. Planck’s Radiation Law
The exchange of energy by radiation with
matters do not takes place in continuous
manner but discretely as an integral multiple
of energy E=hv, where h is the Planck’s
constant.
On the basis of his assumption Planck
derived a relation for energy density u(λ) of
resonators emitting radiation of wavelength
lying between λ and λ + d λ as
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
Max Planck
6. Photoelectric Effect
The emission, or ejection, of electrons
(Photoelectrons) from the surface of,
generally, a metal in response to incident
light is called photoelectric effect.
This Phenomenon was observed by Lenard
but explained by Albert Einstein in 1905,
by describing light as composed of discrete
quanta, now called photon, rather than
continuous waves.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
Albert Einstein
7. Dual Nature of Radiation
Matter mass
momentum
Two object can’t exist together at same time and place
Wavelength
Frequency
Two wave co-exist together at same time and place
Matter
Wave
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
8. de – Broglie Hypothesis
In his 1924, depending on the
source doctoral dissertation, the
French physicist Louis de Broglie
made a bold assertion that just as
light has both wave-like and
particle-like properties, electrons
also have wave-like properties
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
9. de – Broglie Relation
λ = h/p
Wave Particle
By rearranging the momentum equation stated in the
above section, we find a relationship between
the wavelength, λ associated with an electron and
its momentum, p, through the Planck constant, h:
λ = h/p
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
10. Matter Wave
• A wave associated with the motion of a particle e of atomic
or subatomic size that describes effects such as the diffraction
of beams of particles by crystals.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
11. Wave Packet
• wave packet is a combination of waves with about the same momentum.
• Combining waves into wave packets can provide localization of particles.
• The envelope of the wave packet shows the region where the particle is
likely to be found.
• This region propagates with the classical particle velocity.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
12. Heisenberg's Uncertainty
Principle
The uncertainty principle also called
the Heisenberg Uncertainty
Principle, or Indeterminacy
Principle, articulated (1927) by the
German physicist Werner
Heisenberg, that the position and
the velocity of an object cannot
both be measured exactly, at the
same time.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
13. Heisenberg's Uncertainty
Principle
• The product of the uncertainties in the
momentum and the position of a particle
equals h/(2) or more.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
14. Group Velocity
• The group velocity is dω/dk . It describes how
fast wave packets move. It is the velocity with
which the envelop of the wave packet moves
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
Group Velocity
Phase Velocity
15. Phase Velocity
• The velocity of the component waves of a
wave packet is called Phase velocity.
• The phase velocity is ω/k . It describes how
fast the individual wave moves.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
16. Dependency on the medium
• phase velocity vp of waves are typically larger than the
group velocity vg of waves. However, this really
depends on the properties of the medium.
• The media in which vg = vp is called the non-dispersive
medium.
• The media in which vg < vp is called normal dispersive
medium.
• The media in which vg > vp is called anomolous
dispersive media.
• It must be emphasized that dispersion is a property of
the medium in which a wave travels. It is not the
property of the waves themselves.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
17. Wave Function
• It is variable quantity that mathematically describes
the wave characteristics of a particle.
• The value of the wave function of a particle at a given
point of space and time is related to the likelihood of
the particle’s being there at the time.
• By analogy with waves such as those of sound, a wave
function, designated by the Greek letter psi, Ψ, may be
thought of as an expression for the amplitude of the
particle wave (or de Broglie wave), although for such
waves amplitude has no physical significance.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
18. Physical interpretation of wave
function
• The wave function, at a particular time, contains all the
information that anybody at that time can have about the
particle.
• But the wave function itself has no physical interpretation.
• It is not measurable. However, the square of the absolute
value of the wave function has a physical
interpretation. We interpret |ψ(x,t)|2 as a probability
density, a probability per unit length of finding the particle
at a time t at position x.
• The probability of finding the particle at time t in an
interval ∆x about the position x is proportional to
|ψ(x,t)|2∆x.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
19. Schrödinger Equation
• Schrödinger equation is a linear, second order partial
differential equation.
• It is a wave equation in terms of the wave function
which predicts analytically the probability of the
properties the system or events or outcome with
precision.
• The Schrödinger equation is a more general and
fundamental postulate of quantum physics.
• It plays the same role in quantum physics which
Newton's laws and the conservation of energy play in
classical physics i.e., it predicts the time evolution i.e.
future behavior of a quantum dynamical system.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
20. • An important feature of the Schrödinger
equation is that it is linear. Hence it allows for
the superposition of its solutions i.e. wave
functions.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
21 ba
21. • The Schrodinger equation has two forms’, one in which
time explicitly appears, and so describes how the wave
function of a particle will evolve in time. In general, the
wave function behaves like a, wave, and so the
equation is, often referred to as time dependent
Schrodinger wave equation.
• The other is the equation in which the time
dependence has been removed and hence is known as
the time independent Schrodinger equation and is
found to describe, amongst other things, what the
allowed energies are of the particle.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
22. Schrödinger Time Independent
Equation
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
0
8
2
2
2
2
VE
h
m
x
Wave function
Second derivative
wrt x
Position
Energy
Potential Energy
Schrodinger established his equation based on de Broglie’s Hypothesis of
matter wave, Classical plane wave equation & Conservation of Energy.
23. Schrödinger Time Dependent
Equation
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
V
mt
i
2
2
2
•The TDSE is consistent with energy conservation.
•The TDSE is linear and singular value, which implies
that solutions can be constructed by superposition of
two or more independent solutions.
•The free-particle solution (U(x) = 0) is consistent with a
single de Broglie wave.
25. Spontaneous and Stimulated
Emission
• Stimulated Absorption: An atom in a lower
level absorbs a photon of frequency hν and
moves to an upper level.
• Spontaneous Emission: An atom in an upper
level can decay spontaneously to the lower
level and emit a photon of frequency hν if the
transition between E2 and E1 is radiative. This
photon has a random direction and phase.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
27. Stimulated Emission
• An incident photon causes an upper level
atom to decay, emitting a “stimulated” photon
whose properties are identical to those of the
incident photon.
• The term “stimulated” underlines the fact that
this kind of radiation only occurs if an incident
photon is present.
• The amplification arises due to the similarities
between the incident and emitted photons.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
29. Metasatable State
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
It is excited state of an atom,
nucleus, or other system that has a
longer lifetime than the ordinary
excited states and that generally has
a shorter lifetime than the lowest,
often stable, energy state, called the
ground state.
It has a life time between 10-3 to 10-5
sec.
30. Population Inversion
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
It is the process in which the
population of upper energy
level is increased in
comparison to lower energy
level. It is used obtain optical
amplification via stimulated
emission needed for laser
action.
31. Laser Gain
• It is defined as the amount of stimulated emission in
which a can generate as it travels a given distance in
the laser medium.
• It is characterised by the ability of laser medium to
increase the intensity of power of laser.
• It is also the measure of degree of amplification.
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
32. Q M in Real Life
1/28/2017 DR MD KALEEM/ AISSISTANT PROFESSOR
At bottom, the entire computer industry is built on
quantum mechanics.
Modern semiconductor-based electronics rely on
the band structure of solid objects. This is fundamentally
a quantum phenomenon, depending on the wave nature
of electrons, and because we understand that wave
nature, we can manipulate the electrical properties of
silicon.
The fibers themselves are pretty classical, but the light
sources used to send messages down the fiber optic
cables are lasers, which are quantum devices.