# Quantum Mechanics

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## Book Description

*A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics*

Continuing to offer an exceptionally clear, up-to-date treatment of the subject, **Quantum Mechanics, Sixth Edition** explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics.

**New to the Sixth Edition**

- Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book
- Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically
- Additional end-of-chapter problems with different ranges of difficulty

This exemplary text shows students how cutting-edge theoretical topics are applied to a variety of areas, from elementary atomic physics and mathematics to angular momentum and time dependence to relativity and quantum computing. Many examples and exercises illustrate the principles and test students’ understanding.

## Table of Contents

** Waves, Electromagnetism, and the Limits of Classical PhysicsThe Physics and Mathematics of Waves **A REVIEW OF SIMPLE HARMONIC MOTION

THE STRETCHED STRING EQUATION OF MOTION

STANDING WAVES AND FOURIER SERIES

THE FOURIER TRANSFORM PROBLEMS

**Maxwell’s Equation and Electromagnetic Waves **MAXWELL’S EQUATIONS AS INTEGRALS

SURFACE THEOREMS IN VECTOR CALCULUS

MAXWELL’S EQUATION AS DERIVATIVES

ELECTROMAGNETIC WAVES

ELECTROMAGNETIC RADIATION

**Particle Mechanics, Relativity, and Photons**

NEWTON, MAXWELL, AND EINSTEIN

SPACETIME IN SPECIAL RELATIVITY

VELOCITY, MOMENTUM, AND ENERGY

**The Early Development of Quantum Mechanics **THE PHOTOELECTRIC EFFECT

THE COMPTON EFFECT

LINE SPECTRA AND ATOMIC STRUCTURE

DE BROGLIE WAVES

WAVE-PARTICLE DUALITY

THE REST OF THIS BOOK

*Elementary Wave Mechanics*The One-Dimensional Schrödinger Equations

THE TIME-DEPENDENT SCHRÖDINGER EQUATION

THE TIME-INDEPENDENT SCHRÖDINGER EQUATION

BOUNDARY CONDITIONS

THE INFINITE SQUARE WELL

THE FINITE SQUARE WELL

QUANTUM MECHANICAL TUNNELLING

THE HARMONIC OSCILLATOR

**The Three-Dimensional Schrödinger Equations**THE WAVE EQUATIONS

SEPARATION IN CARTESIAN COORDINATES

SEPARATION IN SPHERICAL POLAR COORDINATES

THE HYDROGENIC ATOM

** Formal FoundationsThe Basic Postulates of Quantum Mechanics**THE WAVE FUNCTION

THE DYNAMICAL VARIABLES

PROBABILITY DISTRIBUTIONS

COMMUTATION RELATIONS

THE UNCERTAINTY PRINCIPLE

THE TIME DEPENDENCE OF THE WAVE FUNCTION

DEGENERACY

THE HARMONIC OSCILLATOR AGAIN

THE MEASUREMENT OF MOMENTUM BY COMPTON SCATTERING

**Angular Momentum I **

THE ANGULAR-MOMENTUM OPERATORS

THE ANGULAR MOMENTUM EIGENVALUES AND EIGENFUNCTIONS

THE EXPERIMENTAL MEASUREMENT OF ANGULAR MOMENTUM

A GENERAL SOLUTION TO THE ANGULAR MOMENTUM EIGENVALUE PROBLEM

**Angular Momentum II **MATRIX REPRESENTATIONS

PAULI SPIN MATRICES

SPIN AND THE QUANTUM THEORY OF MEASUREMENT

DIRAC NOTATION

SPIN-ORBIT COUPLING AND THE ZEEMAN EFFECT

A MORE GENERAL TREATMENT OF THE COUPLING OF ANGULAR MOMENTA

**Time-Independent Perturbation Theory and the Variational Principle**

PERTURBATION THEORY FOR NONDEGENERATE ENERGY LEVELS

PERTURBATION THEORY FOR DEGENERATE ENERGY LEVELS

THE VARIATIONAL PRINCIPLE

*Extensions and Approximation Schemes*Time Dependence

TIME-INDEPENDENT HAMILTONIANS

THE SUDDEN APPROXIMATION

TIME-DEPENDENT PERTURBATION THEORY

TRANSITIONS BETWEEN ATOMIC ENERGY LEVELS

THE EHRENFEST THEOREM

THE AMMONIA MASER

**Scattering **

SCATTERING IN ONE DIMENSION

SCATTERING IN THREE DIMENSIONS

THE BORN APPROXIMATION

PARTIAL WAVE ANALYSIS

**Many-Particle Systems **

GENERAL CONSIDERATIONS

ISOLATED SYSTEMS

NONINTERACTING PARTICLES

INDISTINGUISHABLE PARTICLES

MANY-PARTICLE SYSTEMS

THE HELIUM ATOM

SCATTERING OF IDENTICAL PARTICLES

**Relativity and Quantum Mechanics**

BASIC RESULTS IN SPECIAL RELATIVITY

THE DIRAC EQUATION

ANTIPARTICLES

OTHER WAVE EQUATIONS

QUANTUM FIELD THEORY AND THE SPIN-STATISTICS THEOREM

** Advanced TopicsQuantum Information **QUANTUM CRYPTOGRAPHY

ENTANGLEMENT

CLONING AND TELEPORTATION

QUANTUM COMPUTING

**The Conceptual Problems of Quantum Mechanics**

THE CONCEPTUAL PROBLEMS

HIDDEN-VARIABLE THEORIES

NONLOCALITY

THE QUANTUM MEASUREMENT PROBLEM

THE ONTOLOGICAL PROBLEM

*Problems appear at the end of each chapter.*

## Author(s)

### Biography

**Alastair I.M. Rae** retired as a reader in quantum physics from the University of Birmingham. He first taught quantum mechanics in the 1970s, which led to the publication of the first edition of this book. He has conducted research in many areas of condensed matter physics, including superconductivity and its "high temperature" manifestations.

**Jim Napolitano** is a professor of physics at Temple University. His research field is experimental nuclear and particle physics, focusing primarily on studies of fundamental interactions. He also is interested in modern instructional techniques and has published two textbooks on advanced topics in physics.

## Reviews

"The sixth edition of Alastair Rae’s

Quantum Mechanics(co-authored by Jim Napolitano) is a valid undergraduate-level introductory text. Well suited for students in Chemistry, Materials Science, and Engineering…now the book is divided into 5 conceptual "Parts", which helps teachers in selecting only the topics which are more suitable for the background of their students… Chapter 15, indeed, provides an accessible introduction to present-day "hot" research areas (quantum cryptography, quantum computing, teleportation), even working out some simple but intriguing examples, likely to stimulate further interest in Quantum Mechanics…the last chapter of the book deals with conceptual problems in Quantum Mechanics. Here authors present a beautiful, in-depth analysis of the concept of quantum measurement, analyzing consequences also at the philosophical level."

—Francesco Montalenti, Università di Milano Bicocca, inIl Nuovo Saggiatore, Vol 33, anno 2017, no. 3-4"This is a great introductory text to quantum mechanics with thorough explanations of the derivations. Several introductory chapters are especially useful to students with a weak background in physics. The material is well presented and contains numerous worked out problems and application examples. This can be a good reference book for modern physics laboratory classes as well."

—Professor V.F. Mitrovic, Brown University"I expect this book will become a very popular and valuable text for students and instructors alike in undergraduate quantum mechanics. In part one, the authors give a helpful review of the physics—from classical waves to special relativity—that provides the necessary foundations for learning quantum mechanics. Together, parts two, three, and four then offer well-structured, splendidly written, and comprehensive coverage of undergraduate quantum mechanics, from the Schrödinger equation and its various applications, through the postulates and the formalism, to spin, perturbation theory, many-particle systems, and a very nice introduction on relativistic quantum theory. Part four provides a unique and enjoyable tour of selected advanced topics, including quantum computing and conceptual issues within quantum theory. Along the way, the authors incorporate a good number of worked examples. The end-of-chapter problems are well chosen to help with student learning. … both students and instructors will greatly appreciate this instructive, comprehensive, and gorgeously written text."

—Tim Gorringe,Professor of Physics, University of Kentucky"This text provides an updated treatment of quantum mechanics, suitable for the standard senior-level undergraduate course at U.S. colleges and universities. The text has many worked examples and a full topic coverage, including Maxwell’s equations (which is a topic often left out of competing textbooks). Notable features are the section on indistinguishable particles, applications such as MRI and superconductivity, and scattering (which students often have difficulty with)."

—Dr. Pete Markowitz,Professor, Department of Physics, Florida International University"The new sixth edition of this well-known textbook should be thought of as one of the best options available for undergraduate quantum mechanics courses, among a very large class of introductory books. New sections, which review the physics of waves, electricity and magnetism, and special relativity, lay the groundwork for the following chapters, which span the range from traditional quantum mechanics topics (the 1D time-independent Schrödinger equation, hydrogenic atoms, angular momentum theory, and time-independent and time-dependent perturbation theory) to more advanced topics, including scattering theory, the Dirac equation, and new topics in quantum information theory. Detailed worked examples and asides on associated applications of the principles discussed (including the physical basis of magnetic resonance imaging, electron microscopy, and scanning tunneling microscopy) enhance the educational aspects of this book."

—Aaron Lindenberg, Associate Professor, Department of Materials Science and Engineering/Photon Science, Stanford University/SLAC National Accelerator Laboratory"There are many excellent quantum mechanics textbooks on the market. The book by Rae and Napolitano distinguishes itself with a unique approach by including more materials on practical applications of the theoretical concepts detailed in the text. This book can be a great choice of textbook for upper class undergraduate students in physics or students entering graduate studies in engineering schools."

—Professor Chunhui Chen,Iowa State University"This is a very versatile textbook, which could be used in a variety of courses ranging from an ‘honors’ introductory course to a challenging undergraduate upper-class course. Concise but very readable reviews of classical waves, electromagnetism, and relativity are provided. The coverage of quantum mechanics spans elementary wave mechanics, formal theory, perturbation theory, and the Dirac equation. The book is divided into parts, making it easy for an instructor to choose the relevant material based on the level of the class."

—Robert Pelcovits,Professor of Physics, Brown University