Quantum Mechanics I : The Fundamentals book cover
SAVE
$23.00
1st Edition

Quantum Mechanics I
The Fundamentals




ISBN 9780429194566
Published December 11, 2014 by CRC Press
613 Pages

What are VitalSource eBooks?




Prices & shipping based on shipping country


Preview

Book Description

Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems.

The text addresses many topics not typically found in books at this level, including:

  • Bound state solutions of quantum pendulum
  • Pöschl–Teller potential
  • Solutions of classical counterpart of quantum mechanical systems
  • A criterion for bound state
  • Scattering from a locally periodic potential and reflection-less potential
  • Modified Heisenberg relation
  • Wave packet revival and its dynamics
  • Hydrogen atom in D-dimension
  • Alternate perturbation theories
  • An asymptotic method for slowly varying potentials
  • Klein paradox, Einstein-Podolsky-Rosen (EPR) paradox, and Bell’s theorem
  • Numerical methods for quantum systems

A collection of problems at the end of each chapter develops students’ understanding of both basic concepts and the application of theory to various physically important systems. This book, along with the authors’ follow-up Quantum Mechanics II: Advanced Topics, provides students with a broad, up-to-date introduction to quantum mechanics.

Print Versions of this book also include access to the ebook version.

Table of Contents

Why Was Quantum Mechanics Developed?
INTRODUCTION
BLACK BODY RADIATION
PHOTOELECTRIC EFFECT
HYDROGEN SPECTRUM
FRANCK–HERTZ EXPERIMENT
STERN–GERLACH EXPERIMENT
CORRESPONDENCE PRINCIPLE
COMPTON EFFECT
SPECIFIC HEAT CAPACITY
DE BROGLIE WAVES
PARTICLE DIFFRACTION
WAVE-PARTICLE DUALITY

Schrödinger Equation and Wave Function
INTRODUCTION
CONSTRUCTION OF SCHRÖDINGER EQUATION
SOLUTION OF TIME-DEPENDENT EQUATION
PHYSICAL INTERPRETATION OF ψ∗ψ
CONDITIONS ON ALLOWED WAVE FUNCTIONS
BOX NORMALIZATION
CONSERVATION OF PROBABILITY
EXPECTATION VALUE
EHRENFEST’S THEOREM
BASIC POSTULATES
TIME EVOLUTION OF STATIONARY STATES
CONDITIONS FOR ALLOWED TRANSITIONS
ORTHOGONALITY OF TWO STATES
PHASE OF THE WAVE FUNCTION
CLASSICAL LIMIT OF QUANTUM MECHANICS

Operators, Eigenvalues, and Eigenfunctions
INTRODUCTION
LINEAR OPERATORS
COMMUTING AND NONCOMMUTING OPERATORS
SELF-ADJOINT AND HERMITIAN OPERATORS
DISCRETE AND CONTINUOUS EIGENVALUES
MEANING OF EIGENVALUES AND EIGENFUNCTIONS
PARITY OPERATOR
ALL HERMITIAN HAMILTONIANS HAVE PARITY
SOME OTHER USEFUL OPERATORS

Exactly Solvable Systems I: Bound States
INTRODUCTION
CLASSICAL PROBABILITY DISTRIBUTION
FREE PARTICLE
HARMONIC OSCILLATOR
PARTICLE IN THE POTENTIAL V (x) = x2k, k = 1, 2, · · ·
PARTICLE IN A BOX
PÖSCHL–TELLER POTENTIALS
QUANTUM PENDULUM
CRITERIA FOR THE EXISTENCE OF A BOUND STATE
TIME-DEPENDENT HARMONIC OSCILLATOR
RIGID ROTATOR

Exactly Solvable Systems II: Scattering States
INTRODUCTION
POTENTIAL BARRIER: TUNNEL EFFECT
FINITE SQUARE-WELL POTENTIAL
POTENTIAL STEP
LOCALLY PERIODIC POTENTIAL
REFLECTIONLESS POTENTIALS
DYNAMICAL TUNNELING

Matrix Mechanics
INTRODUCTION
LINEAR VECTOR SPACE
MATRIX REPRESENTATION OF OPERATORS AND WAVE FUNCTION
UNITARY TRANSFORMATION
TENSOR PRODUCTS
SCHRÖDINGER EQUATION AND OTHER QUANTITIES IN MATRIX FORM
APPLICATION TO CERTAIN SYSTEMS
DIRAC’S BRA AND KET NOTATIONS
EXAMPLES OF BASIS IN QUANTUM THEORY
PROPERTIES OF KET AND BRA VECTORS
HILBERT SPACE
PROJECTION AND DISPLACEMENT OPERATORS

Various Pictures and Density Matrix
INTRODUCTION
SCHRÖDINGER PICTURE
HEISENBERG PICTURE
INTERACTION PICTURE
COMPARISON OF THREE REPRESENTATIONS
DENSITY MATRIX FOR A SINGLE SYSTEM
DENSITY MATRIX FOR AN ENSEMBLE
TIME EVOLUTION OF DENSITY OPERATOR
A SPIN-1/2 SYSTEM

Heisenberg Uncertainty Principle
INTRODUCTION
THE CLASSICAL UNCERTAINTY RELATION
HEISENBERG UNCERTAINTY RELATION
IMPLICATIONS OF UNCERTAINTY RELATION
ILLUSTRATION OF UNCERTAINTY RELATION
THE MODIFIED HEISENBERG RELATION

Momentum Representation
INTRODUCTION
MOMENTUM EIGENFUNCTIONS
SCHRÖDINGER EQUATION
EXPRESSIONS FOR hXi AND hpi
TRANSFORMATION BETWEEN MOMENTUM AND COORDINATE REPRESENTATIONS
OPERATORS IN MOMENTUM REPRESENTATION
MOMENTUM FUNCTION OF SOME SYSTEMS

Wave Packet
INTRODUCTION
PHASE AND GROUP VELOCITIES
WAVE PACKETS AND UNCERTAINTY PRINCIPLE
GAUSSIAN WAVE PACKET
WAVE PACKET REVIVAL
ALMOST PERIODIC WAVE PACKETS

Theory of Angular Momentum
INTRODUCTION
SCALAR WAVE FUNCTION UNDER ROTATIONS
ORBITAL ANGULAR MOMENTUM
EIGENPAIRS OF L2 AND Lz
PROPERTIES OF COMPONENTS OF L AND L2
EIGENSPECTRA THROUGH COMMUTATION RELATIONS
MATRIX REPRESENTATION OF L2, Lz AND L±
WHAT IS SPIN?
SPIN STATES OF AN ELECTRON
SPIN-ORBIT COUPLING
ROTATIONAL TRANSFORMATION
ADDITION OF ANGULAR MOMENTA
ROTATIONAL PROPERTIES OF OPERATORS
TENSOR OPERATORS
THE WIGNER–ECKART THEROEM

Hydrogen Atom
INTRODUCTION
HYDROGEN ATOM IN THREE-DIMENSION
HYDROGEN ATOM IN D-DIMENSION
FIELD PRODUCED BY A HYDROGEN ATOM
SYSTEM IN PARABOLIC COORDINATES

Approximation Methods I: Time-Independent Perturbation Theory
INTRODUCTION
THEORY FOR NONDEGENERATE CASE
APPLICATIONS TO NONDEGENERATE LEVELS
THEORY FOR DEGENERATE LEVELS
FIRST-ORDER STARK EFFECT IN HYDROGEN
ALTERNATE PERTURBATION THEORIES

Approximation Methods II: Time-Dependent Perturbation Theory
INTRODUCTION
TRANSITION PROBABILITY
CONSTANT PERTURBATION
HARMONIC PERTURBATION
ADIABATIC PERTURBATION
SUDDEN APPROXIMATION
THE SEMICLASSICAL THEORY OF RADIATION
CALCULATION OF EINSTEIN COEFFICIENTS

Approximation Methods III: WKB and Asymptotic Methods
INTRODUCTION
PRINCIPLE OF WKB METHOD
APPLICATIONS OF WKB METHOD
WKB QUANTIZATION WITH PERTURBATION
AN ASYMPTOTIC METHOD

Approximation Methods IV: Variational Approach
INTRODUCTION
CALCULATION OF GROUND STATE ENERGY
TRIAL EIGENFUNCTIONS FOR EXCITED STATES
APPLICATION TO HYDROGEN MOLECULE
HYDROGEN MOLECULE ION

Scattering Theory
INTRODUCTION
CLASSICAL SCATTERING CROSS-SECTION
CENTRE OF MASS AND LABORATORY COORDINATES SYSTEMS
SCATTERING AMPLITUDE
GREEN’S FUNCTION APPROACH
BORN APPROXIMATION
PARTIAL WAVE ANALYSIS
SCATTERING FROM A SQUARE-WELL SYSTEM
PHASE-SHIFT OF ONE-DIMENSIONAL CASE
INELASTIC SCATTERING

Identical Particles
INTRODUCTION
PERMUTATION SYMMETRY
SYMMETRIC AND ANTISYMMETRIC WAVE FUNCTIONS
THE EXCLUSION PRINCIPLE
SPIN EIGENFUNCTIONS OF TWO ELECTRONS
EXCHANGE INTERACTION
EXCITED STATES OF THE HELIUM ATOM
COLLISIONS BETWEEN IDENTICAL PARTICLES

Relativistic Quantum Theory
INTRODUCTION
KLEIN–GORDON EQUATION
DIRAC EQUATION FOR A FREE PARTICLE
NEGATIVE ENERGY STATES
JITTERY MOTION OF A FREE PARTICLE
SPIN OF A DIRAC PARTICLE
PARTICLE IN A POTENTIAL
KLEIN PARADOX
RELATIVISTIC PARTICLE IN A BOX
RELATIVISTIC HYDROGEN ATOM
THE ELECTRON IN A FIELD
SPIN-ORBIT ENERGY

Mysteries in Quantum Mechanics
INTRODUCTION
THE COLLAPSE OF THE WAVE FUNCTION
EINSTEIN–PODOLSKY–ROSEN (EPR) PARADOX
HIDDEN VARIABLES
THE PARADOX OF SCHRÖDINGER’S CAT
BELL’S THEOREM
VIOLATION OF BELL’S THEOREM
RESOLVING EPR PARADOX

Numerical Methods for Quantum Mechanics
INTRODUCTION
MATRIX METHOD FOR COMPUTING STATIONARY STATE SOLUTIONS
FINITE-DIFFERENCE TIME-DOMAIN METHOD
TIME-DEPENDENT SCHRÖDINGER EQUATION
QUANTUM SCATTERING
ELECTRONIC DISTRIBUTION OF HYDROGEN ATOM
SCHRÖDINGER EQUATION WITH AN EXTERNAL FIELD

Appendix A: Calculation of Numerical Values of h and kB
Appendix B: A Derivation of the Factor h_/(eh_/kBT − 1)
Appendix C: Bose’s Derivation of Planck’s Law
Appendix D: Distinction between Self-Adjoint and Hermitian Operators
Appendix E: Proof of Schwarz’s Inequality
Appendix F: Eigenvalues of a Symmetric Tridiagonal Matrix—QL Method
Appendix G: Random Number Generators for Desired Distributions

Solutions to Selected Exercises

Index

Concluding Remarks, Bibliography, and Exercises appear at the end of each chapter.

...
View More

Author(s)

Biography

S. Rajasekar received his B.Sc. and M.Sc. in physics both from the St. Joseph’s College, Tiruchirapalli. In 1987, he received his M.Phil. in physics from Bharathidasan University, Tiruchirapalli. He was awarded a Ph.D. in physics (nonlinear dynamics) from Bharathidasan University in 1992. In 2005, he became a professor at the School of Physics, Bharathidasan University. His recent research focuses on nonlinear dynamics with a special emphasis on nonlinear resonances. He has coauthored a book, and authored or coauthored more than 80 research papers in nonlinear dynamics.

R. Velusamy received his B.Sc. in physics from the Ayya Nadar Janaki Ammal College, Sivakasi in 1972 and M.Sc. in physics from the P.S.G. Arts and Science College, Coimbatore in 1974. He received an M.S. in electrical engineering at the Indian Institute of Technology, Chennai in the year 1981. In the same year, he joined in the Ayya Nadar Janaki Ammal College as an assistant professor in physics. He was awarded an M.Phil. in physics in 1988. He retired in 2010. His research topics are quantum confined systems and wave packet dynamics.

Reviews

"The first volume of this course of quantum mechanics contains basic concepts of quantum mechanics, mathematical formalism, and a wide range of applications to physically important systems. The problems concerning the considered subject are included at the end of each chapter. The textbook is intended for graduate students and also as a reference book. Doubtless advantage of this tutorial is the discussion of such mysteries in quantum mechanics as the collapse of the wave function, Einstein-Podolsky-Rosen paradox, hidden variables, the paradox of Schrödinger cat, and Bell's theorem. It should be noted the presence of numerical methods in quantum mechanics."
Zentralblatt MATH 1318

"… excellent, up-to-date … can be used as either a two-to-three-semester graduate text or as a standalone reference book. Quantum Mechanics I: The Fundamentals covers the canonical basics and Quantum Mechanics II: Advanced Topics covers a range of modern developments from introductory quantum field theory through quantum information theory and other quantum technologies, such as quantum metrology and imaging, that are not discussed in other sources … I recommend this set highly."
—Dr. Jonathan P. Dowling, Hearne Professor of Theoretical Physics and Co-Director, Hearne Institute for Theoretical Physics, Louisiana State University, and Author of Schrödinger's Killer App: Race to Build the World's First Quantum Computer

"Be assured … these two books by Rajasekar and Velusamy will definitely tell you how to do quantum mechanics."
—Dr. K.P.N. Murthy, Professor, School of Physics, and Director, Centre for Integrated Studies, University of Hyderabad

Vol I quote: "The real strength of this book lies in its scope. Each individual chapter covers the fundamentals of a topic and acts as an excellent reference for quantum researchers….I will certainly ensure that a copy remains on my bookshelf, for when I have a query on any fundamental aspect of quantum mechanics."
Contemporary Physics (Nov 2017), review by Prof. Thomas Collier, University of Exeter

Vol II quote: "I found digesting the latter part of this book a most enjoyable experience. Indeed, the final chapters on broad applications of advanced quantum mechanics are entertaining to read and refrain from delving too deeply into the intricacies. The reader is given an enticing glimpse of the research directions one might apply the knowledge of quantum mechanics presented over the two volumes. As with the first volume, I will keep this book close at hand for when I require a concise and mathematically rich guide to these advanced topics of quantum mechanics."
Contemporary Physics (Nov 2017), review by Prof. Thomas Collier, University of Exeter

Support Material

Ancillaries

  • Instructor Resources

    To gain access to the instructor resources for this title, please visit the Instructor Resources Download Hub.

    You will be prompted to fill out a regist