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
The postulates of quantum mechanics have been successfully used for deriving exact solutions to Schrodinger equation for problems like A particle in 1 Dimensional box Harmonic oscillator Rigid rotator Hydrogen atom • However for a multielectron system, the SWE cannot be solved exactly due to inter-electronic repulsion terms.
The SWE is solved by method of seperation of variables.
• However, the inter-electronic repulsion term cannot be solved because the variables cannot be seperated and the SWE cannot be solved. • Approximate methods have helped to generate solutions for such and even more complex real quantum systems. • Approximate methods have been developed for solving Schrodinger equation to find wave function and energy of the complex system under consideration. • Two widely used approximate methods are, 1. Perturbation theory 2. Variation method
Perturbation theory is an approximate method that describes a complex quantum system in terms of a simpler system for which the exact solution is known. • Perturbation theory has been categorized into, i. Time independent perturbation theory, proposed by Erwin Schrodinger, where the perturbation Hamiltonian is static. ii. Time dependent perturbation theory, proposed by Paul Dirac, which studies the effect of time dependent perturbation on a time independent Hamiltonian H0.
PERTURBATION THEOREM
FIRST ORDER PERTURBATION THEORY
FIRST ORDER ENERGY CORRECTION
FIRST ORDER WAVE FUNCTION CORRECTION
APPLICATIONS OF PERTURBATION METHOD
SIGNIFICANCE OF PERTURBATION METHOD
Schrodinger equation and its applications: Chapter 2Dr.Pankaj Khirade
Wave function and its physical significance, Schrodinger time dependent equation, Separation in time dependent and time independent parts, Operators in quantum Mechanics, Eigen functions and Eigen values, Particle in one dimensional and three dimensional box (Energy eigen values). Qualitative analysis of potential barrier Tunneling effect). Simple Harmonic Oscillator (Qualitative analysis of Zero point energy)
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
The postulates of quantum mechanics have been successfully used for deriving exact solutions to Schrodinger equation for problems like A particle in 1 Dimensional box Harmonic oscillator Rigid rotator Hydrogen atom • However for a multielectron system, the SWE cannot be solved exactly due to inter-electronic repulsion terms.
The SWE is solved by method of seperation of variables.
• However, the inter-electronic repulsion term cannot be solved because the variables cannot be seperated and the SWE cannot be solved. • Approximate methods have helped to generate solutions for such and even more complex real quantum systems. • Approximate methods have been developed for solving Schrodinger equation to find wave function and energy of the complex system under consideration. • Two widely used approximate methods are, 1. Perturbation theory 2. Variation method
Perturbation theory is an approximate method that describes a complex quantum system in terms of a simpler system for which the exact solution is known. • Perturbation theory has been categorized into, i. Time independent perturbation theory, proposed by Erwin Schrodinger, where the perturbation Hamiltonian is static. ii. Time dependent perturbation theory, proposed by Paul Dirac, which studies the effect of time dependent perturbation on a time independent Hamiltonian H0.
PERTURBATION THEOREM
FIRST ORDER PERTURBATION THEORY
FIRST ORDER ENERGY CORRECTION
FIRST ORDER WAVE FUNCTION CORRECTION
APPLICATIONS OF PERTURBATION METHOD
SIGNIFICANCE OF PERTURBATION METHOD
Schrodinger equation and its applications: Chapter 2Dr.Pankaj Khirade
Wave function and its physical significance, Schrodinger time dependent equation, Separation in time dependent and time independent parts, Operators in quantum Mechanics, Eigen functions and Eigen values, Particle in one dimensional and three dimensional box (Energy eigen values). Qualitative analysis of potential barrier Tunneling effect). Simple Harmonic Oscillator (Qualitative analysis of Zero point energy)
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
It contains the basic principle of Mossbauer Spectroscopy.
Recoil energy, Dopler shift.
The instrumentation of Mossbauer Spectroscopy.
Hyperfine interactions.
NQR - DEFINITION - ELECTRIC FIELD GRADIENT - NUCLEAR QUADRUPOLE MOMENT - NUCLEAR QUADRUPOLE COUPLING CONSTANT - PRINCIPLE OF NQR - ENERGY OF INTERACTION - SELECTION RULE - FREQUENCY OF TRANSITION - APPLICATIONS
CONTENTS
INTRODUCTION
CONCEPTS OF WALSH DIAGRAM
APPLICATION IN TRIATOMIC MOLECULES
[IN AH₂ TYPE OF MOLECULES(BeH₂,BH₂,H₂O)]
INTRODUCTION
Arthur Donald Walsh FRS The introducer of walsh diagram (8 August 1916-23 April 1977) was a British chemist, professor of chemistry at the University of Dundee . He was elected FRS in 1964. He was educated at Loughborough Grammar School.
Walsh diagrams were first introduced in a series of ten papers in one issue of the Journal of the Chemical Society . Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken .
It contains the basic principle of Mossbauer Spectroscopy.
Recoil energy, Dopler shift.
The instrumentation of Mossbauer Spectroscopy.
Hyperfine interactions.
NQR - DEFINITION - ELECTRIC FIELD GRADIENT - NUCLEAR QUADRUPOLE MOMENT - NUCLEAR QUADRUPOLE COUPLING CONSTANT - PRINCIPLE OF NQR - ENERGY OF INTERACTION - SELECTION RULE - FREQUENCY OF TRANSITION - APPLICATIONS
CONTENTS
INTRODUCTION
CONCEPTS OF WALSH DIAGRAM
APPLICATION IN TRIATOMIC MOLECULES
[IN AH₂ TYPE OF MOLECULES(BeH₂,BH₂,H₂O)]
INTRODUCTION
Arthur Donald Walsh FRS The introducer of walsh diagram (8 August 1916-23 April 1977) was a British chemist, professor of chemistry at the University of Dundee . He was elected FRS in 1964. He was educated at Loughborough Grammar School.
Walsh diagrams were first introduced in a series of ten papers in one issue of the Journal of the Chemical Society . Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken .
Ch2 mathematical modeling of control system Elaf A.Saeed
Chapter 2 Mathematical modeling of control system From the book (Ogata Modern Control Engineering 5th).
2-1 introduction.
2-2 transfer function and impulse response function.
2-3 automatic control systems.
Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively
ME-314 Introduction to Control Engineering is a course taught to Mechanical Engineering senior undergrads. The course is taught by Dr. Bilal Siddiqui at DHA Suffa University. This lecture is about modeling electrical and mechanical systems (transnational and rotational) in frequency domain.
Kane’s Method for Robotic Arm Dynamics: a Novel ApproachIOSR Journals
Abstract: This paper is the result of Analytical Research work in multi-body dynamics and desire to apply
Kane’s Method on the Robotic Dynamics. The Paper applies Kane’s method (originally called Lagrange form
of d’Alembert’s principle) for developing dynamical equations of motion and then prepare a solution scheme for
space Robotics arms. The implementation of this method on 2R Space Robotic Arm with Mat Lab Code is
presented in this research paper. It is realized that the limitations and difficulties that are aroused in arm
dynamics are eliminated with this novel Approach.
Key Words: Dynamics, Equation of Motion, Lagrangian, , Robotic arm, Space Robot,
ABSTRACT : In this paper, the simulation of a double pendulum with numerical solutions are discussed. The double pendulums are arranged in such a way that in the static equilibrium, one of the pendulum takes the vertical position, while the second pendulum is in a horizontal position and rests on the pad. Characteristic positions and angular velocities of both pendulums, as well as their energies at each instant of time are presented. Obtained results proved to be in accordance with the motion of the real physical system. The differentiation of the double pendulum result in four first order equations mapping the movement of the system.
An Introductory review for use of Eigenvalues in Quantum Mechanics
An operator acting on a function, changes functions into another function. Occasionally
there are instances where, the received function is directly proportional to the function used.
퐴(휓) ∝ 휓
In this type of a situation, a constant, 푎 can be defined, as the Eigenvalue of the function. The
operator, 퐴 is hence known as an Eigen operator.
퐴(휓) = 푎휓
The 푎 eigenvalues represents the possible measured values of the 퐴 operator.
Classically, 푎 would be allowed to vary continuously, but in quantum mechanics, 푎 typically
has only a sub-set of allowed values. Both time-dependent and time-independent Schrödinger
equations are the `best-known instances of an eigenvalue equations in quantum mechanics, with
its eigenvalues corresponding to the allowed energy levels of the quantum system. (“3.3: The
Schrödinger Equation is an Eigenvalue Problem - Chemistry LibreTexts,” n.d.)
Some Eigen operators used in quantum mechanics and what their eigen constants represent are
given below.
(“Operators in Quantum Mechanics,” n.d.)The left side of the above table denotes the physical meaning of Eigen value obtained when
relevant operator on the right side is applied on the wave equation giving the position of the a
quantum particle. A famous example denoting the Energy of a particle when Hamiltonian
operator is applied on the wave function, is given below.
(“The Hamiltonian Operator | My Blog,” n.d.
we are introduce here, the history of benzene, introduction, description, structure review, key points, applications, effects on human life, bibliography
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
3. The First Two Postulates of Quantum
Mechanics
• The Schrödinger equation does not provide a complete theory of
quantum mechanics.
• Schrödinger, Heisenberg, and others devised several
postulates(unproved fundamental assumptions) that form a
consistent logical foundation for nonrelativistic quantum mechanics.
• In any theory based on postulates, the validity of the postulates is
tested by comparing the consequences of the postulates with
experimental fact. The postulates of quantum mechanics do pass this
test.
4. Postulate 1
• All information that can be obtained about the state of a mechanical
system is contained in a wave function Ψ, which is a continuous,
finite, and single-valued function of time and of the coordinates of
the particles of the system
5. Explanation
• This postulate implies that there is a one-to-one relationship between the
state of the system and a wave function. That is, each possible state
corresponds to one wave function, and each possible wave function
corresponds to one state.
• The terms “state function” and “wave function” are often used
interchangeably.
• Information about values of mechanical variables such as energy and
momentum must be obtained from the wave function, instead of from
values of coordinates and velocities as in classical mechanics.
• The fourth postulate will provide the method for obtaining this
information.
6. Postulate 2
• The wave function Ψ obeys the time-dependent Schrödinger
equation.
• where H is the Hamiltonian operator of the system.
7. • The time-independent Schrödinger equation can be derived from the
time-dependent equation, by assuming that the wave function is a
product of a coordinate factor and a time factor:
• Where q stands for all of the coordinates of the particles in the
system and where the coordinate wave function ψ satisfies the time-
independent Schrödinger equation.
• Not all wave functions consist of the two factors in Eq., but all wave
functions must obey the time-dependent Schrödinger equation.
8. The Third Postulate. Mathematical Operators
and Mechanical Variables
• The time-independent Schrödinger equation determines the energy
eigenvalues for a given system.
• These eigenvalues are the possible values that the energy of the
system can take on.
• The third and fourth postulates must be used to obtain the possible
values of other mechanical variables such as the momentum and the
angular momentum.
• The third postulate is:
9. Postulates 3
• There is a linear hermitian mathematical operator in one-to-one correspondence with every mechanical
variable.
• This postulate states that for each operator there is one and only one variable, and
• for each variable there is one and only one mathematical operator.
• A mathematical operator is a symbol that stands for performing one or more
mathematical operations.
• When the symbol for an operator is written to the left of the symbol for a function, the
operation is to be applied to that function.
• For example, d/dx is a derivative operator, standing for differentiation of the function
with respect to x; c is a multiplication operator, standing for multiplication of the function
by the constant c; h(x) is also a multiplication operator, standing for multiplication by the
function h(x).
10. Cont:
• denote an operator by a letter with a caret ( ) over it.
• The result of operating on a function with an operator is another
function. If A is an operator and f is a function,
• Where g is another function. The symbol q is an abbreviation for
whatever independent variables f and g depend on. shows an
example of a function, f(x)=ln(x),
• and the function g(x)=1/x that results when the operator d/dx is
applied to ln(x).
11.
12. Hermitian operator
• Hermitian operators have several important properties:
1. Hermitian operators are linear.
2. Two hermitian operators are not required to commute with each other.
3. A hermitian operator has a set of eigenfunctions and eigenvalues.
4. The eigenvalues of a hermitian operator are real.
5. Two eigenfunctions of a hermitian operator with different eigenvalues are
orthogonal to each other.
6. Two commuting hermitian operators can have a set of common
eigenfunctions.
7. The set of eigenfunctions of a hermitian operator form a complete set for
expansion of functions obeying the same boundary conditions.
13. Postulate 4 and Expectation Values
• The first postulate of quantum mechanics asserts that the wave
function of a system contains all available information about the
values of mechanical variables for the state corresponding to the
wave function.
• The third postulate provides a mathematical operator for each
mechanical variable.
• The fourth postulate provides the mathematical procedure for
obtaining the available information:
14. Postulate 4
• (a) If a mechanical variable A is measured without experimental error, the
only possible outcomes of the measurement are the eigenvalues of the
operator A that corresponds to A.
• (b) Thee expectation value for the error-free measurement of a mechanical
variable A if given by the formula
• where3 A is the operator corresponding to the variable A, and where
ψ=ψ(q, t)is the wave function corresponding to the state of the system at
the time of the measurement.
15. Postulate 5. Measurements and
the Determination of the State of a System
• The fifth and final postulate gives information about the state of a
system following a measurement.
• Postulate 5. Immediately after an error-free measurement of the
mechanical variable A in which the outcome was the eigenvalue aj,
the state of the system corresponds to a wave function that is an
eigenfunction of A with eigenvalue equal to aj.
16. Explanations
• This postulate says very little about the state of the system prior to a
single measurement of the variable A, because the act of
measurement can change the state of the system.
• To understand physically how a measurement can change the state of
a system consider the determination of the position of a particle by
the scattering of electromagnetic radiation. When an airplane reflects
a radar wave, the effect on the airplane is negligible because of the
large mass of the airplane. When an object of small mass such as an
electron scatters ultraviolet light or X-rays, the effect is not negligible.