1st Edition

Quantum Mechanics
Foundations and Applications





ISBN 9780367390501
Published October 23, 2019 by CRC Press
343 Pages 58 B/W Illustrations

USD $74.95

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Book Description

Progressing from the fundamentals of quantum mechanics (QM) to more complicated topics, Quantum Mechanics: Foundations and Applications provides advanced undergraduate and graduate students with a comprehensive examination of many applications that pertain to modern physics and engineering.

Based on courses taught by the author, this textbook begins with an introductory chapter that reviews historical landmarks, discusses classical theory, and establishes a set of postulates. The next chapter demonstrates how to find the appropriate wave functions for a variety of physical systems in one dimension by solving the Schrödinger equation where for time-independent cases, the total energy is an eigenvalue. The following chapter extends this method to three dimensions, focusing on partial differential equations. In subsequent chapters, the author develops the appropriate operators, eigenvalues, and eigenfunctions for angular momentum as well as methods for examining time-dependent systems. The final chapters address special systems of interest, such as lasers, quarks, and hadrons. Appendices offer additional material, exploring matrices, functions, and physical constants.

Relating theory with experiment, Quantum Mechanics: Foundations and Applications provides both basic and complex information for junior- and senior-level physics and engineering students.

Table of Contents

Preface

THE FOUNDATIONS OF QUANTUM PHYSICS
The Prelude to Quantum Mechanics
Wave-Particle Duality and the Uncertainty Relation
Fourier Transforms in Quantum Mechanics
The Postulatory Basis of Quantum Mechanics
Operators and the Mathematics of Quantum Mechanics
Properties of Quantum Mechanical Systems

THE SCHRÖDINGER EQUATION IN ONE DIMENSION
The Free Particle
One-Dimensional Harmonic Oscillator
Time Evolution and Completeness
Operator Method

THE SCHRÖDINGER EQUATION IN THREE DIMENSIONS
The Free Particle in Three Dimensions
Particle in a Three-Dimensional Box
The One-Electron Atom
Central Potentials

TOTAL ANGULAR MOMENTUM
Orbital and Spin Angular Momentum
Half-Integral Spin Angular Momentum
Addition of Angular Momenta
Interacting Spins for Two Particles

APPROXIMATION METHODS
Introduction - The Many-Electron Atom
Nondegenerate Perturbation Theory
Perturbation Theory for Degenerate States
Time-Dependent Perturbation Theory
The Variational Method
Wentzel, Kramers, and Brillouin Theory (WKB)

ATOMIC SPECTROSCOPY
Effects of Symmetry
Spin-Orbit Coupling in Multielectron Atoms

QUANTUM STATISTICS
Derivation of the Three Quantum Distribution Laws
Applications of the Quantum Distribution Laws

BAND THEORY OF SOLIDS
Periodic Potentials
Periodic Potential - Kronig-Penney Model
Impurities in Semiconductors
Drift, Diffusion, and Recombination
Semiconductor Devices

EMISSION, ABSORPTION, AND LASERS
Emission and Absorption of Photons
Spontaneous Emission
Stimulated Emission and Lasers

SCATTERING THEORY
Scattering in Three Dimensions
Scattering and Inverse Scattering in One Dimension

RELATIVISTIC QUANTUM MECHANICS AND PARTICLE THEORY
Dirac Theory of the Electron
Quantum Electrodynamics (QED) and Electroweak Theory
Quarks, Leptons, and the Standard Model

Appendix A: Matrix Operations
Appendix B: Generating Functions
Appendix C: Answers to Selected Problems
Appendix D: The Fundamental Physical Constants, 1986

Bibliography
Index

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Author(s)

Biography

Swanson, Donald Gary

Reviews

"This textbook on quantum mechanics is characterized by the wide variety of topics touched upon, especially in connection with applications. In fact besides covering essentially all basic arguments for a one year course in quantum mechanics the text briefly considers many other applications such as atomic spectroscopy, quantum statistics, band theory of solids, emission, absorption, lasers, quarks and linear potentials."

– Bassano Vacchini, in Zentralblatt Math, 2009