John David Jackson - Jackson, John David

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Résumé :

Preface ix

About the Companion Website xi

1 Basics 1

1.1 Wave Mechanics of de Broglie and Schr?dinger 1

1.2 Klein-Gordon Equation 2

1.3 Non-Relativistic Approximation 2

1.4 Free-Particle Probability Current 3

1.5 Expectation Values 4

1.6 Particle in a Static, Conservative Force Field 6

1.7 Ehrenfest Theorem 6

1.8 Schr?dinger Equation in Momentum Space 8

1.9 Spread in Time of a Free-Particle Wave Packet 8

1.10 The Nature of Solutions to the Schr?dinger Equation 9

1.11 A Bound-State Problem: Linear Potential 10

1.12 Sturm-Liouville Eigenvalue Problem 11

1.13 Linear Operators on Functions 13

1.14 Eigenvalue Problem for a Hermitian Operator 14

1.15 Variational Methods for Energy Eigenvalues 14

1.16 Rayleigh-Ritz Method 16

Problems 18

2 Reformulation 21

2.1 Stern-Gerlach Experiment 22

2.2 Linear Vector Spaces 22

2.3 Linear Operators 25

2.4 Unitary Transformations of Operators 27

2.5 Generalized Uncertainty Relation for Self-Adjoint Operators 27

2.6 Infinite-Dimensional Vector Spaces - Hilbert Space 28

2.7 Assumptions of Quantum Mechanics 29

2.8 Mixtures and the Density Matrix 30

2.9 Measurement 32

2.10 Classical vs. Quantum Probabilities 33

2.11 Capsule Review of Classical Mechanics and Conservation Laws 34

2.12 Translation Invariance and Momentum Conservation 37

2.13 Dirac's p's and q's 38

2.14 Time Development of the State Vector 41

2.15 Schr?dinger and Heisenberg Pictures 42

2.16 Simple Harmonic Oscillator 46

Problems 51

3 Wentzel-Kramers-Brillouin (WKB) Method 55

3.1 Semi-classical Approximation 55

3.2 Solution in One Dimension 56

3.3 Schr?dinger Equation for the Linear Potential 58

3.4 Connection Formulae for the WKB Method 63

3.5 WKB Formula for Bound States 65

3.6 Example of WKB with a Power Law Potential 67

3.7 Normalization of WKB Bound State Wave Functions 68

3.8 Bohr's Correspondence Principle and Classical Motion 68

3.9 Power of WKB 72

3.10 Barrier Penetration with the WKB Method 73

3.11 Symmetrical Double-Well Potential 75

3.12 Application of the WKB Method to Ammonia Molecule 79

Problems 80

4 Rotations, Angular Momentum, and Central Force Motion 85

4.1 Infinitesimal Rotations 85

4.2 Construction of Irreducible Representations 88

4.3 Coordinate Representation of Angular Momentum Eigenvectors 91

4.4 Observation of Sign Change for Rotation by 2? 92

4.5 Euler Angles, Wigner d-functions 95

4.6 Application to Nuclear Magnetic Resonance 98

4.7 Addition of Angular Momenta 104

4.8 Integration Over the Rotation Group 106

4.9 Gaunt Integral 108

4.10 Tensor Operators 109

4.11 Wigner-Eckart Theorem 112

4.12 Applications of the Wigner-Eckart Theorem 114

4.13 Two-Body Central Force Motion 118

4.14 The Coulomb Problem 121

4.15 Patterns of Bound States 125

4.16 Hellmann-Feynman Theorem 127

Problems 128

5 Time-Independent Perturbation Theory 135

5.1 Time-Independent Perturbation Expansion 135

5.2 Interlude: Spectra and History 137

5.3 Fine Structure of Hydrogen 139

5.4 Stark Effect in Ground-State Hydrogen 141

5.5 Perturbation Theory with Degeneracy 143

5.6 Linear Stark Effect in Hydrogen 145

5.7 Perturbation Theory with Near Degeneracy 146

5.8 Zeeman and Paschen-Back Effects in Hydrogen 149

Problems 149

6 Atomic Structure 151

6.1 Parity 1...

Biographie:

John David Jackson (1925-2016) was a revered physics professor at the University of California, Berkeley, a faculty Senior Scientist at Lawrence Berkeley National Laboratory, and a member of the National Academy of Sciences. A theoretical physicist, he is well known for numerous publications and summer-school lectures in nuclear and particle physics, as well as for his definitive text, Classical Electrodynamics.

Robert N. Cahn is Senior Scientist, emeritus, at the Lawrence Berkeley National Laboratory. He has conducted research in theoretical and experimental particle physics and cosmology. The co-author, with Gerson Goldhaber, of the text Experimental Foundations of Particle Physics, he has taught physics at both the undergraduate and graduate levels....

Sommaire:
derivations and calculations come with clearly explained steps. More than 120 figures illustrate underlying principles, experimental apparatus, and data.

In A Course in Quantum Mechanics readers will find detailed treatments of:

• Wave mechanics of de Broglie and Schr?dinger, the Klein-Gordon equation and its non-relativistic approximation, free particle probability current, expectation values.
• Schr?dinger equation in momentum space, spread in time of a free-particle wave packet, density matrix, Sturm-Liouville eigenvalue problem.
• WKB formula for bound states, example of WKB with a power law potential, normalization of WKB bound state wave functions, barrier penetration with WKB.
• Rotations and angular momentum, representations, Wigner d-functions, addition of angular momenta, the Wigner-Eckart theorem.
• Time-independent perturbation theory, Stark, Zeeman, Paschen-Back effects, time-dependent perturbation theory, Fermi's Golden Rule.
• Atomic structure, helium, multiplet structure, Russell-Saunders coupling, spin-orbit interaction, Thomas-Fermi model, Hartree-Fock approximation.
• Scattering amplitude, Born approximation, allowing internal structure, inelastic scattering, optical theorem, validity criterion for the Born approximation, partial wave analysis, eikonal approximation, resonance.
• Semi-classical and quantum electromagnetism, Aharonov-Bohm effect, Lagrangian and Hamiltonian formulations, gauge invariance, quantization of the electromagnetic field, coherent states.
• Emission and absorption of radiation, dipole transitions, selection rules, Weisskopf-Wigner treatment of line breadth and level shift, Lamb shift.
• Relativistic quantum mechanics, Klein-Gordon equation, Dirac equation, two-component reduction, hole theory, Foldy-Wouthuysen transformation, Lorentz covariance, discrete symmetries, non-relativistic and relativistic Compton scattering.