Quantum Mechanics

Front Cover
Title Page
© 2000 Springer Science+BusÎness Media New York
Preface
Contents
Part I Introduction to Quantum Mechanics
1 Background: The Duality of Nature
2 The Motion of Wave Packets: Fourier Analysis
3 The Schrödinger Wave Equation and Probability Interpretation
4 Schrödinger Theory: The Existence of Discrete Energy Levels
5 Harmonic Oscillator Calculations
6 Further Interpretation of the WaveFunction
7 The Eigenvalue Problem
8 Spherical Harmonics, Orbital Angular Momentum
9 i-Step operators for the () Equation
10 The Radial Functions for the Hydrogenic Atom
11 Shape-Invariant Potentials: Soluble One-Dimensional Potential Problems
12 The Darboux Method: Supersymmetric Partner Potentials
13 The Vector Space Interpretation of Quantum-Mechanical Systems
14 The Angular Momentum Eigenvalue Problem (Revisited)
15 Rigid Rotators: Molecular Rotational Spectra
16 Transformation Theory
17 Another Example: Successive Polarization Filters for Beams of Spin s =1/2 Particles
18 Transfonnation Theory for Systems with Continuous Spectra
19 Time-Dependence of State Vectors, Algebraic Techniques, Coherent States
Part II Time-Independent Perturbation Theory
20 Perturbation Theory
21 Stationary -State Perturbation Theory
22 Example 1: The Slightly Anharmonic Oscillator
23 Perturbation Theory for Degenerate Levels
24 The Case of Nearly Degenerate Levels
25 Magnetic Field Perturbations
26 Fine Structure and Zeeman Perturbations in Alkali Atoms
Part III Angular Momentum Theory
27 Angular Momentum Coupling Theory
28 Symmetry Properties of Clebsch-Gordan Coefficients
29 Invariance of Physical Systems Under Rotations
30 The Clebsch-Gordan Series
31 Spherical Tensor Operators
32 The Wigner-Eckart Theorem
33 Nuclear Hyperfine Structure in One-Electron Atoms
34 Angular Momentum Recoupling: Matrix Elements of Coupled Tensor Operators in an Angular Momentum Coupled Basis
35 Perturbed Coulomb Problems via SO(2, 1) Algebra
36 The WKB Approximation
37 Applications of the WKB Approximation
Part IV Systems of Identical Particles
38 The Two-Electron Atom
39 n-Identical Particle States
40 The Variational Method
Part V Scattering Theory
41 Introduction to Scattering Theory
42 The Rayleigh-Faxen-Holtzmark Partial Wave Expansion: Phase Shift Method
43 A Specific Example: Scattering from Spherical Square Well Potentials
44 Scattering Resonances: Low-Energy Scattering
45 Integral Equation for Two-Body Relative Motion: Scattering Green's Functions in Coordinate Representation
46 The Born Approximation
47 Operator Form of Scattering Green's Function and the Integral Equation for the Scattering Problem
48 Inelastic Scattering Processes and Rearrangement Collisions
49 Differential Scattering Cross Sections for Rearrangement Collisions: Born Approximation
50 A Specific Example of a Rearrangement Collision: The (d, p) Reaction on Nucleus A
51 The S Matrix
52 Scattering Theory for Particles with Spin
53 Scattering of Spin 1/2 Particles from Spinless Target: Partial Wave Decomposition
54 The Polarization Vector
55 Density Matrices
56 Isospin
Part VI Time-Dependent Perturbation Theory
57 Time-Dependent Perturbation Expansion
58 Oscillating Magnetic Fields: Magnetic Resonance
59 Sudden and Adiabatic Approximations
Part VII Atom-Photon Interactions
60 Interaction of Electromagnetic Radiation with Atomic Systems
61 Photons: The Quantized Radiation Field
62 Vector Spherical Harmonics
63 The Emission of Photons by Atoms: Electric Dipole Approximation
64 The Photoelectric Effect: Hydrogen Atom
65 Spontaneous Photon Emission: General Case: Electric and Magnetic Multipole Radiation
66 Scattering of Photons by Atomic Systems
67 Resonance Fluorescence Cross Section
68 Natural Line Width: Wigner-Weisskopf Treatment
Part VIII Introduction to Relativistic Quantum Mechanics
69 Dirac Theory: Relativistic Quantum Theory of Spin-1/2 Particles
70 Lorentz Covariance of the Dirac Equation
71 Bilinear Covariants
72 Simple Solutions: Free Particle Motion: Plane Wave Solutions
73 Dirac Equation for a Particle in an Electromagnetic Field
74 Pauli Approximation to the Dirac Equation
75 The Klein Paradox: An Example from the History of Negative Energy State Difficulties: The Positron Interpretation
76 Exact Solutions for the Dirac Equation for Spherically Symmetric Potentials
77 The MIT Bag Model: The Dirac Equation for a Quark Confined to a Spherical Region
Part IX Introduction to Many-Body Theory
78 Many-Body Formalism
79 Many-Body Techniques: Some Simple Applications
Index