QUANTUM MECHANICS (2ND ED): An Accessible Introduction

by Robert Scherrer

Overview

This book provides a comprehensive introduction to quantum mechanics from the ground up. It is designed to be completely self-contained and assumes very little knowledge or mathematical background on the part of students as it takes them through the major topics of quantum mechanics.

Designed to be appropriate for students across a wide range of abilities and backgrounds, this book will be particularly helpful for students who might lack some of the mathematical background typically assumed in an undergraduate quantum mechanics course. The book includes three 'math interludes' covering such topics as complex numbers, linear operators, vector spaces, and matrix manipulation. The book also discusses some interesting modern applications of quantum mechanics: magnetic resonance imaging and quantum computing, and it concludes with an introduction to relativistic quantum theory.

This second edition includes expanded and improved coverage of the Heisenberg uncertainty principle, the use of ladder operators to solve the harmonic oscillator, as well as the treatment of the Lamb shift.

Contents:

• The Origins of Quantum Mechanics
• Math Interlude A: Complex Numbers and Linear Operators
• The Schrödinger Equation
• Solutions of the One-Dimensional Time-Independent Schrödinger Equation
• Math Interlude B: Linear Algebra
• Solutions of the Three-Dimensional Time-Independent Schrödinger Equation
• Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function
• Spin Angular Momentum
• Time-Independent Perturbation Theory
• The Variational Principle
• Time-Dependent Perturbation Theory
• Scattering Theory
• Multiparticle Schrödinger Equation
• Modern Applications of Quantum Mechanics
• Relativistic Quantum Mechanics

Readership: Undergraduate students, useful for all Physics majors and some Engineering majors; Educators of undergrad students.

Key Features:

• Designed to be appropriate for students with a wide range of abilities and backgrounds
• Helpful for students who might lack some of the mathematical background typically assumed in a quantum mechanics course
• Includes three math interludes" covering such topics as complex numbers, linear operators, vector spaces, and matrix manipulation
• Also discusses some interesting modern applications of quantum mechanics: magnetic resonance imaging and quantum computing, and concludes with an introduction to relativistic quantum theory

Product Details

ISBN-13:	9789811286742
Publisher:	WSPC
Publication date:	03/19/2024
Sold by:	Barnes & Noble
Format:	eBook
Pages:	384
File size:	28 MB
Note:	This product may take a few minutes to download.

About the Author

Robert Scherrer is Chair of the Department of Physics and Astronomy at Vanderbilt University, where he arrived in 2003 following 15 years as a professor of physics at Ohio State University. He received is A.B. in physics from Princeton University, spent two years at Cambridge University on a Marshall Scholarship, and then received his Ph.D. in physics at the University of Chicago. While a professor at Ohio State, Scherrer received the Alumni Award for Distinguished Teaching. His teaching philosophy follows the advice of Hippocrates: “First, do no harm.” He believes that most physics students come to study physics because they find it interesting, and it is the teacher’s job to maintain that interest while navigating the sometimes-difficult subject matter.

Scherrer’s own research is in the area of theoretical cosmology, including the physics of the early universe, dark matter and dark energy, and the large-scale structure of the universe. He lives in Nashville, Tennessee with his wife and five children.

Table of Contents

Table of Contents

1. The Origins of Quantum Mechanics

1.1 Introduction

1.2 Blackbody Radiation

The Problem with Blackbody Radiation

1.3 The Nature of Light

The Photoelectric Effect

The Compton Effect

Is it a Particle or a Wave?

1.4 TheWave Nature of Matter

1.5 The Bohr Atom

1.6 Where do we Stand?

2. Math Interlude A: Complex Numbers and Linear Operators

2.1 Complex Numbers

2.2 Operators

Definition of an Operator

Eigenfunctions and Eigenvalues

3. The Schrödinger Equation

3.1 Derivation of the Schrödinger Equation

3.2 The Meaning of theWave Function

3.3 The Time-Independent Schrödinger Equation

Derivation of the Time-Independent Schrödinger Equation

Qualitative Solutions and the Origin of Quantization

4. One-Dimensional Time-Independent

Schrödinger Equation

4.1 Unbound States: Scattering and Tunneling

Scattering From Step-Function Potentials

4.2 Bound Systems

The Infinite SquareWell

The Harmonic Oscillator Potential

5. Math Interlude B: Linear Algebra

5.1 Properties of Linear Operators

5.2 Vector Spaces

Inner Products

Adjoint and Hermitian Operators

Basis Sets

6. The Three-Dimensional Time-Independent

Schrödinger Equation

6.1 Solution in Rectangular Coordinates

6.2 Angular Momentum

6.3 The Schrödinger Equation in Spherical Coordinates

6.4 The Hydrogen Atom

7. Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function

7.1 The Matrix Formulation of Linear Operators

7.2 Dirac Notation

7.3 The Dirac Delta Function

8. Spin Angular Momentum

8.1 Spin Operators

8.2 Evidence for Spin

8.3 Adding Angular Momentum

8.4 The Matrix Representation of Spin

8.5 The Stern–Gerlach Experiment

8.6 Spin Precession

8.7 Spin Systems with Two Particles

Noninteracting Spins

Interacting Spins

8.8 Measurement Theory

Hidden Variables

The ManyWorlds Interpretation of Quantum Mechanics

9. Time-Independent Perturbation Theory

9.1 Derivation of Time-Independent Perturbation Theory

9.2 Perturbations to the Atomic Energy Levels

Fine Structure

The Lamb Shift

9.3 The Atom in External Electric or Magnetic Fields

The Atom in an Electric Field: The Stark Effect

The Atom in a Magnetic Field: The Zeeman Effect

10. The Variational Principle

10.1 Variational Principle: Theory

10.2 Variational Principle: Application to the Helium Atom

11. Time-Dependent Perturbation Theory

11.1 Derivation of Time-Dependent Perturbation Theory

11.2 Application: Selection Rules for Electromagnetic Radiation

12. Scattering Theory

12.1 Definition of the Cross Section

12.2 The Born Approximation

12.3 PartialWaves

13. The Multiparticle Schrödinger Equation

13.1 Wave Function for Identical Particles

13.2 Multielectron Atoms

14. Some Modern Applications of Quantum Mechanics

14.1 Magnetic Resonance Imaging

14.2 Quantum Computing

15. What Comes Next? Relativistic Quantum Mechanics

15.1 The Klein–Gordon Equation

Derivation of the Klein–Gordon Equation

Probability Densities and Currents

15.2 The Dirac Equation

Answers and Hints for Selected End-of-Chapter Exercises

Index