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PART Ⅰ ELEMENTARY PRINCIPLES AND APPLICATIONS TO PROBLEMS IN ONE DIMENSION 3

Chapter 1Review of Concepts of Classical Mechanics 3

1.1Generalized or “Good” Coordinates 3

1.2Energy，the Hamiltonian， and Angular Momentum 6

1.3The State of a System 19

1.4Properties of the One-Dimensional Potential Function 24

Chapter 2Historical Review：Experiments and Theories 28

2.1Dates 28

2.2The Work of Planck.Blackbody Radiation 29

2.3The Work of Einstein.The Photoelectric Effect 34

2.4The Work of Bohr. A Quantum Theory of Atomic States 38

2.5Waves versus Particles 41

2.6The de Broglie Hypothesis and the Davisson-Germer Experiment 44

2.7The Work of Heisenberg. Uncertainty as a Cornerstone of Natural Law 51

2.8The Work of Born.Probability Waves 53

2.9Semiphilosophieal Epilogue to Chapter 255

Chapter 3The Postulates of Quantum Mechanics.Operators，Eigenfunetions，and Eigenvalues 64

3.1Observables and Operators 64

3.2Measurement in Quantum Mechanics 70

3.3The State Function and Expectation Values 73

3.4Time Development of the State Function 77

3.5Solution to the Initial-Value Problem in Quantum Mechanics 81

Chapter 4 Preparatory Concepts.Function Spaces and Hermitian Operators 86

4.1Particle in a Box and Further Remarks on Normalization 86

4.2 The Bohr Correspondence Principle 91

4.3Dirac Notation 93

4.4Hilbert Space 94

4.5Hermitian Operators 100

4.6Properties of Hermitian Operators 104

Chapter 5 Superposition and Compatible Observables 109

5.1The Superposition Principle 109

5.2Commutator Relations in Quantum Mechanics 124

5.3More on the Commutator Theorem 131

5.4Commutator Relations and the Uncertainty Principle 134

5.5“Complete” Sets of Commuting Observables 137

Chapter 6 Tine Development，Conservation Theorems，and Parity 143

6.1Time Development of State Functions 143

6.2Time Development of Expectation Values 159

6.3Conservation of Energy. Linear and Angular Momentum 163

6.4Conservation of Parity 167

Chapter 7 Additional One-Dimne??i?al Problems.Bound and Unbound States 176

7.1General Properties of the One-Dimensional Schr？dinger Equation 176

7.2The Harmonic Oscillator 179

7.3Eigenfunetions of the Harmonic Oscillator Hamiltonian 187

7.4The Harmonic Oscillator in Momentum Space 199

7.5Unbound States 204

7.6One-Dimensional Barrier Problems 211

7.7The Rectangular Barrier.Tunneling 217

7.8The Ramsauer Effect 224

7.9Kinetic Properties of a Wave Packet Scattered from a Potential Barrier 230

7.10The WKB Approximation 232

Chapter 8 Finite Potential Well，Periodic Lattice，and Some Simple Problems with Two Degrees of Freedom 256

8.1The Finite Potential Well 256

8.2Periodic Lattice. Energy Gaps 267

8.3Standing Waves at the Band Edges 284

8.4Brief Qualitative Description of the Theory of Conduction in Solids 291

8.5Two Beads on a Wire and a Particle in a Two-Dimensional Box 294

8.6Two-Dimensional Harmonic Oscillator 300

PART Ⅱ FURTHER DEVELOPMENT OF THE THEORY AND APPLICATIONS TO PROBLEMS IN THREE DIMNSIONS 309

Chapter 9 Angular Momentum 309

9.1Basic Properties 310

9.2Eigenvalues of the Angular Momentum Operators 318

9.3Eigenfunctions of the Orbital Angular Momentum Operators Lz and Lz 326

9.4 Addition of Angular Momentum 345

9.5Total Angular Momentum for Two or More Electrons 353

Chapter 10 Problems in Three Dimensions 359

10.1The Free Particle in Cartesian Coordinates 359

10.2The Free Particle in Spherical Coordinates 365

10.3The Free-Particle Radial Wavefunction 370

10.4A Charged Particle in a Magnetic Field 380

10.5The Two-Particle Problem 383

10.6The Hydrogen Atom 394

10.7Elementary Theory of Radiation 410

Chapter 11 Elements of Matrix Mechanics.Spin Wavefunctions 418

11.1Basis and Representations 418

11.2Elementary Matrix Properties 426

11.3Unitary and Similarity Transformations in Quantum Mechanics 439

11.4The Energy Representation 436

11.5Angular Momentum Matrices 442

11.6The Pauli Spin Matrices 450

11.7Free-Particle Wavefunctions， Including Spin 455

11.8The Magnetic Moment of an Electron 457

11.9Precession of an Electron in a Magnetic Field 465

11.10The Addition of Two Spins 474

11.11The Density Matrix 481

Chapter 12 Application to Atomic and Molecular Physics.Elements of Quantum Statistics 491

12.1The Total Angular Momentum，J 491

12.2One-Electron Atoms 496

12.3The Pauli Principle 508

12.4The Periodic Table 514

12.5The Slater Determinant 520

12.6Application of Symmetrization Rules to the Helium Atom 523

12.7The Hydrogen and Deuterium Molecule 532

12.8Brief Description of Quantum Models for Superconductivity and Superfluidity 539

Chapter 13 Perturbation Theory 549

13.1Time-Independent，Nondegenerate Perturbation Theory 549

13.2Time-Independent， Degenerate Perturbation Theory 560

13.3The Stark Effect 568

13.4The Nearly Free Electron Model 571

13.5Time-Dependent Perturbation Theory 576

13.6Harmonic Perturbation 579

13.7Application of Harmonic Perturbation Theory 585

13.8Selective Perturbations in Time 594

Chapter 14 Scattering in Three Dimensions 605

14.1Partial Waves 605

14.2S-Wave Scattering 613

14.3Center-of-Mass Frame 617

14.4The Born Approximation 621

List of Symbols 627

Appendixes 633

AAdditional Remarks on the ？and？Representations 633

BSpin and Statistics 637

CRepresentations of the Delta Function 639

DPhysical Constants and Equivalence（=）Relations 642

Index 645