Schaum's Outline of Quantum Mechanics, Second Edition | Schaum's Outline

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Schaum's Outline of Quantum Mechanics, Second Edition

Schaum's Outline of Quantum Mechanics, Second Edition

Authors: Yoav Peleg, Reuven Pnini, Elyahu Zaarur and Eugene Hecht

Published: May 2010

eISBN: 9780071623599 0071623590 | ISBN: 9780071623582

Contents

Chapter 1 Introduction

1.1 The Particle Nature of Electromagnetic Radiation

1.2 Quantum Particles

1.3 Wave Packets and the Uncertainty Relation

Chapter 2 Mathematical Background

2.1 The Complex Field C

2.2 Vector Spaces over C

2.3 Linear Operators and Matrices

2.4 Eigenvectors and Eigenvalues

2.5 Fourier Series and the Fourier Transform

2.6 The Dirac Delta Function

Chapter 3 The Schrödinger Equation and Its Applications

3.1 Wavefunctions of a Single Particle

3.2 The Schrödinger Equation

3.3 Particle in a Time-Independent Potential

3.4 Scalar Product of Wavefunctions: Operators

3.5 Probability Density and Probability Current

Chapter 4 The Foundations of Quantum Mechanics

4.1 Introduction

4.2 Postulates in Quantum Mechanics

4.3 Mean Value and Root-Mean-Square Deviation

4.4 Commuting Observables

4.5 Function of an Operator

4.6 Hermitian Conjugation

4.7 Discrete and Continuous State Spaces

4.8 Representations

4.9 The Time Evolution

4.10 Uncertainty Relations

4.11 The Schrödinger and Heisenberg Pictures

Chapter 5 Harmonic Oscillator

5.1 Introduction

5.2 The Hermite Polynomials

5.3 Two- and Three-Dimensional Harmonic Oscillators

5.4 Operator Methods for a Harmonic Oscillator

Chapter 6 Angular Momentum

6.1 Introduction

6.2 Commutation Relations

6.3 Lowering and Raising Operators

6.4 Algebra of Angular Momentum

6.5 Differential Representations

6.6 Matrix Representation of an Angular Momentum

6.7 Spherical Symmetry Potentials

6.8 Angular Momentum and Rotations

Chapter 7 Spin

7.1 Definitions

7.2 Spin 1/2

7.3 Pauli Matrices

7.4 Lowering and Raising Operators

7.5 Rotations in the Spin Space

7.6 Interaction with a Magnetic Field

Chapter 8 Hydrogen-like Atoms

8.1 A Particle in a Central Potential

8.2 Two Interacting Particles

8.3 The Hydrogen Atom

8.4 Energy Levels of the Hydrogen Atom

8.5 Mean Value Expressions

8.6 Hydrogen-like Atoms

Chapter 9 Particle Motion in an Electromagnetic Field

9.1 The Electromagnetic Field and Its Associated Potentials

9.2 The Hamiltonian of a Particle in the Electromagnetic Field

9.3 Probability Density and Probability Current

9.4 The Magnetic Moment

9.5 Units

Chapter 10 Solution Methods in Quantum Mechanics—Part A

10.1 Time-Independent Perturbation Theory

10.2 Perturbation of a Nondegenerate Level

10.3 Perturbation of a Degenerate State

10.4 Time-Dependent Perturbation Theory

Chapter 11 Solution Methods in Quantum Mechanics—Part B

11.1 The Variational Method

11.2 Semiclassical Approximation (The WKB Approximation)

Chapter 12 Numerical Methods in Quantum Mechanics

12.1 Numerical Quadrature

12.2 Roots

12.3 Integration of Ordinary Differential Equations

Chapter 13 Identical Particles

13.1 Introduction

13.2 Permutations and Symmetries of Wavefunctions

13.3 Bosons and Fermions

Chapter 14 Addition of Angular Momenta

14.1 Introduction

14.2 {Ĵ[sup(2)][sub(1)], Ĵ[sup(2)][sub(2)], Ĵ[sup(1)][sub(2)]Ĵ[sub(Z)]} Basis

14.3 Clebsch–Gordan Coefficients

Chapter 15 Scattering Theory

15.1 Cross Section

15.2 Stationary Scattering States

15.3 Born Approximation

15.4 Partial Wave Expansions

15.5 Scattering of Identical Particles

Chapter 16 Semiclassical Treatment of Radiation

16.1 The Interaction of Radiation with Atomic Systems

16.2 Time-Dependent Perturbation Theory

16.3 Transition Rate

16.4 Multipole Transitions

16.5 Spontaneous Emission

Appendix: Mathematical Appendix

A.1 Fourier Series and Fourier Transform

A.2 The Dirac d-Function

A.3 Hermite Polynomials

A.4 Legendre Polynomials

A.5 Associated Legendre Functions

A.6 Spherical Harmonics

A.7 Associated Laguerre Polynomials

A.8 Spherical Bessel Functions

Index