《INTRODUCTORY QUANTUM MECHANICS》

PART Ⅰ ELEMENTARY PRINCIPLES AND APPLICATIONS TO PROBLEMS IN ONE DIMENSION3

Chapter 1Review of Concepts of Classical Mechanics3

1.1Generalized or “Good” Coordinates3

1.2Energy，the Hamiltonian， and Angular Momentum6

1.3The State of a System19

1.4Properties of the One-Dimensional Potential Function24

Chapter 2Historical Review：Experiments and Theories28

2.1Dates28

2.2The Work of Planck.Blackbody Radiation29

2.3The Work of Einstein.The Photoelectric Effect34

2.4The Work of Bohr. A Quantum Theory of Atomic States38

2.5Waves versus Particles41

2.6The de Broglie Hypothesis and the Davisson-Germer Experiment44

2.7The Work of Heisenberg. Uncertainty as a Cornerstone of Natural Law51

2.8The Work of Born.Probability Waves53

2.9Semiphilosophieal Epilogue to Chapter255

Chapter 3The Postulates of Quantum Mechanics.Operators，Eigenfunetions，and Eigenvalues64

3.1Observables and Operators64

3.2Measurement in Quantum Mechanics70

3.3The State Function and Expectation Values73

3.4Time Development of the State Function77

3.5Solution to the Initial-Value Problem in Quantum Mechanics81

Chapter 4 Preparatory Concepts.Function Spaces and Hermitian Operators86

4.1Particle in a Box and Further Remarks on Normalization86

4.2 The Bohr Correspondence Principle91

4.3Dirac Notation93

4.4Hilbert Space94

4.5Hermitian Operators100

4.6Properties of Hermitian Operators104

Chapter 5 Superposition and Compatible Observables109

5.1The Superposition Principle109

5.2Commutator Relations in Quantum Mechanics124

5.3More on the Commutator Theorem131

5.4Commutator Relations and the Uncertainty Principle134

5.5“Complete” Sets of Commuting Observables137

Chapter 6 Tine Development，Conservation Theorems，and Parity143

6.1Time Development of State Functions143

6.2Time Development of Expectation Values159

6.3Conservation of Energy. Linear and Angular Momentum163

6.4Conservation of Parity167

Chapter 7 Additional One-Dimne??i?al Problems.Bound and Unbound States176

7.1General Properties of the One-Dimensional Schr？dinger Equation176

7.2The Harmonic Oscillator179

7.3Eigenfunetions of the Harmonic Oscillator Hamiltonian187

7.4The Harmonic Oscillator in Momentum Space199

7.5Unbound States204

7.6One-Dimensional Barrier Problems211

7.7The Rectangular Barrier.Tunneling217

7.8The Ramsauer Effect224

7.9Kinetic Properties of a Wave Packet Scattered from a Potential Barrier230

7.10The WKB Approximation232

Chapter 8 Finite Potential Well，Periodic Lattice，and Some Simple Problems with Two Degrees of Freedom256

8.1The Finite Potential Well256

8.2Periodic Lattice. Energy Gaps267

8.3Standing Waves at the Band Edges284

8.4Brief Qualitative Description of the Theory of Conduction in Solids291

8.5Two Beads on a Wire and a Particle in a Two-Dimensional Box294

8.6Two-Dimensional Harmonic Oscillator300

PART Ⅱ FURTHER DEVELOPMENT OF THE THEORY AND APPLICATIONS TO PROBLEMS IN THREE DIMNSIONS309

Chapter 9 Angular Momentum309

9.1Basic Properties310

9.2Eigenvalues of the Angular Momentum Operators318

9.3Eigenfunctions of the Orbital Angular Momentum Operators Lz and Lz326

9.4 Addition of Angular Momentum345

9.5Total Angular Momentum for Two or More Electrons353

Chapter 10 Problems in Three Dimensions359

10.1The Free Particle in Cartesian Coordinates359

10.2The Free Particle in Spherical Coordinates365

10.3The Free-Particle Radial Wavefunction370

10.4A Charged Particle in a Magnetic Field380

10.5The Two-Particle Problem383

10.6The Hydrogen Atom394

10.7Elementary Theory of Radiation410

Chapter 11 Elements of Matrix Mechanics.Spin Wavefunctions418

11.1Basis and Representations418

11.2Elementary Matrix Properties426

11.3Unitary and Similarity Transformations in Quantum Mechanics439

11.4The Energy Representation436

11.5Angular Momentum Matrices442

11.6The Pauli Spin Matrices450

11.7Free-Particle Wavefunctions， Including Spin455

11.8The Magnetic Moment of an Electron457

11.9Precession of an Electron in a Magnetic Field465

11.10The Addition of Two Spins474

11.11The Density Matrix481

Chapter 12 Application to Atomic and Molecular Physics.Elements of Quantum Statistics491

12.1The Total Angular Momentum，J491

12.2One-Electron Atoms496

12.3The Pauli Principle508

12.4The Periodic Table514

12.5The Slater Determinant520

12.6Application of Symmetrization Rules to the Helium Atom523

12.7The Hydrogen and Deuterium Molecule532

12.8Brief Description of Quantum Models for Superconductivity and Superfluidity539

Chapter 13 Perturbation Theory549

13.1Time-Independent，Nondegenerate Perturbation Theory549

13.2Time-Independent， Degenerate Perturbation Theory560

13.3The Stark Effect568

13.4The Nearly Free Electron Model571

13.5Time-Dependent Perturbation Theory576

13.6Harmonic Perturbation579

13.7Application of Harmonic Perturbation Theory585

13.8Selective Perturbations in Time594

Chapter 14 Scattering in Three Dimensions605

14.1Partial Waves605

14.2S-Wave Scattering613

14.3Center-of-Mass Frame617

14.4The Born Approximation621

List of Symbols627

Appendixes633

AAdditional Remarks on the ？and？Representations633

BSpin and Statistics637

CRepresentations of the Delta Function639

DPhysical Constants and Equivalence（=）Relations642

Index645