PART Ⅰ ELEMENTARY PRINCIPLES AND APPLICATIONS TO PROBLEMS IN ONE DIMENSION

1 Review of Concepts of Classical Mechanics

1.1 Generalized or “Good” Coordinates

1.2 Energy，the Hamiltonian，and Angular Momentum

1.3 The State of a System

1.4 Properties of the One-Dimensional Potential Function

2 Historical Review: Experiments and Theories

2.1 Dates

2.2 The Work of Planck. Blackbody Radiation

2.3 The Work of Einstein. The Photoelectric Effect

2.4 The Work of Bohr. A Quantum Theory of Atomic States

2.5 Waves versus Particles

2.6 The de Broglie Hypothesis and the Davisson-Germer Experiment

2.7 The Work of Heisenberg. Uncertaintu as a Cornerstone of Natural Law

2.8 The Work of Born. Probabiliry Waves

2.9 Semiphilosophical Epilogue to Chapter 2

3 The Postulates of Quantum Mechanics. Operators，Eigenfunctions，and Eigenvalues

3.1 Observables and Operators

3.2 Measurement in Quantum Mechanics

3.3 The State Function and Expectation Values

3.4 Time Development of the State Function

3.5 Solution to the Initial-Value Problem in Quantum Mechanics

4 Preparatory Concepts. Function Spaces and Hermitian Operators

4.1 Particle in a Box and Further Remarks on Normalization

4.2 The Bohr Correspondence Principle

4.3 Dirac Notation

4.4 Hilbert Space

4.5 Hermitian Operators

4.6 Properties of Hermitian Operators

5 Superposition and Compatible Observables

5.1 The Superposition Principle

5.2 Commutator Relations in Quantum Mechanics

5.3 More on the Commutator Theorem

5.4 Commutator Relations and the Uncertainty Principle

5.5 “Complete” Sets of Commuting Observables

6 Time Development，Conservation Theorems，and Parity

6.1 Time Development of State Functions

6.2 Time Development of Expectation Values

6.3 Conservation of Energy，Linear and Angular Momentum

6.4 Conservation of Parity

7 Additional One-Dimensional Problems. Bound and Unbound States

7.1 General Properties of the One-Dimensional Schrodinger Equation

7.2 The Harmonic Oscillator

7.3 Eigenfunctions of the Harmonic Oscillator Hamiltonian

7.4 The Harmonic Oscillator in Momentum Space

7.5 Unbound States

7.6 One-Dimensional Barrier Problems

7.7 The Rectangular Barrier. Tunneling

7.8 The Ramsauer Effect

7.9 Kinetic Properties of a Wave Packet Scattered from a Potential Barrier

7.10 The WKB Approximation

7.11 Principle of Least Action and Feyntnan’s Path Integral Formulation

8 Finite Potential Well，Periodic Lattice，and Some Simple Problems with Two Degrees of Freedom

8.1 The Finite Potential Well

8.2 Periodic Lattice. Energy Gaps

8.3 Standing Waves at the Band Edges

8.4 Brief Qualitative Description of the Theory of Conduction in Solids

8.5 Two Beads on a Wire and a Particle in a Two-Dimensional Box

8.6 Two-Dimensional Harmonic Oscillator

8.7 Linear Combination of Atomic Orbitals （LCAO） Approximation

8.8 Density of States in Various Dimensions

PART Ⅱ FURTHER DEVELOPMENT OF THE THEORY AND APPLICATIONS TO PROBLEMS IN THREE DIMENSIONS

9 Angular Momentum

9.1 Basic Properties

9.2 Eigenvalues of the Angular Momentum Operators

9.3 Eigenfunctions of the Orbital Angular Momentum Operators L2 and Lz

9.4 Addition of Angular Momentum

9.5 Total Angular Momentum for Two or More Electrons

10 Problems in Three Dimensions

10.1 The Free Particle in Cartesian Coordinates

10.2 The Free Particle in Spherical Coordinates

10.3 The Free-Particle Radial Wavefunction

10.4 A Charged Particle in a Magnetic Field

10.5 The Two-Particle Problem

10.6 The Hydrogen Atom

10.7 Elementary Theory of Radiation

10.8 Thomas-Fermi Model

11 Elements of Matrix Mechanics. Spin Wavefunctions

11.1 Basis and Representations

11.2 Elementary Matrix Properties

11.3 Unitary and Similariry Transformations in Quantum Mechanics

11.4 The Energy Representation

11.5 Angular Momentum Matrices

11.6 The Pauli Spin Matrices

11.7 Free-Particle Wavefunctions，Including Spin

11.8 The Magnetic Moment of an Electron

11.9 Precession of an Electron in a Magnetic Field

11.10 The Addition of Two Spins

11.11 The Density Matrix

11.12 Other “Pictures” in Quantum Mechanics

11.13 Polarization States. EPR Revisited

11.14 The Transfer Matrix

12 Application to Atomic，Molecular，Solid-State，and Nuclear Physics. Elements of Quantum Statistics

12.1 The Total Angular Momentum，J

12.2 One-Electron Atoms

12.3 The Pauli Principle

12.4 The Periodic Table

12.5 The Slater Determinant

12.6 Application of Symmetrization Rules to the Helium Atom

12.7 The Hydrogen and Deuterium Molecules

12.8 Brief Description of Quantum Models for Superconductivity and Superfluidity

12.9 Impurity Semiconductors and the p-n Junction

12.10 Elements of Nuclear Physics. The Deuteron and Isospin

13 Perturbation Theory

13.1 Time-Independent，Nondegenerate Perturbation Theory

13.2 Time-Independent，Degenerate Perturbation Theory

13.3 The Stark Effect

13.4 The Nearly Free Electron Model

13.5 Time-Dependent Perturbation Theory

13.6 Harmonic Perturbation

13.7 Application of Harmonic Perturbation Theory

13.8 Selective Perturbations in Time

13.9 Atom-Radiation Interaction

13.10 Hartree-Fock Model

14 Scattering in Three Dimensions

14.1 Partial Waves

14.2 S-Wave Scattering

14.3 Center-of-Mass Frame

14.4 The Born Approximation

14.5 Atomic-Radiative Absorption Cross Section

14.6 Elements of Formal Scattering Theory. The Lippmatm-Schwinger Equation

15 Relativistic Quantum Mechanics

15.1 Preliminary Remarks

15.2 Klein-Gordon Equation

15.3 Dirac Equation

15.4 Electron Magnetic Moment

15.5 Covariant Description

16 Quantum Computing

16.1 Binary Number System

16.2 Logic Gates

16.3 Turing Machine and Complexity Classes

16.4 Qubits and Quantum Logic Gates

List of Symbols

APPENDIXES

A Additional Remarks on the x and p Representations

B Spin and Statistics

C Representations of the Delta Function

D Differential Vector Relations

E Harmonic Oscillator in Spherical Coordinates

F Physical Constants and Equivalence Relations

Index