A Modern Approach to Quantum Mechanics Book

	Preface	xi
1	Stern-Gerlach Experiments	1
1.1	The Original Stern-Gerlach Experiment	1
1.2	Four Experiments	5
1.3	The Quantum State Vector	9
1.4	Analysis of Experiment 3	13
1.5	Experiment 5	15
1.6	Summary	18
2	Rotation of Basis States and Matrix Mechanics	24
2.1	The Beginnings of Matrix Mechanics	24
2.2	Rotation Operators	28
2.3	The Identity and Projection Operators	36
2.4	Matrix Representations of Operators	41
2.5	Changing Representations	45
2.6	Expectation Values	50
2.7	Photon Polarization and the Spin of the Photon	51
2.8	Summary	56
3	Angular Momentum	64
3.1	Rotations Do Not Commute and Neither Do the Generators	64
3.2	Commuting Operators	69
3.3	The Eigenvalues and Eigenstates of Angular Momentum	70
3.4	The Matrix Elements of the Raising and Lowering Operators	77
3.5	Uncertainty Relations and Angular Momentum	78
3.6	The Spin-1/2 Eigenvalue Problem	80
3.7	A Stern-Gerlach Experiment with Spin-1 Particles	85
3.8	Summary	88
4	Time Evolution	93
4.1	The Hamiltonian and the Schrodinger Equation	93
4.2	Time Dependence of Expectation Values	96
4.3	Precession of a Spin-1/2 Particle in a Magnetic Field	97
4.4	Magnetic Resonance	104
4.5	The Ammonia Molecule and the Ammonia Maser	108
4.6	The Energy-Time Uncertainty Relation	115
4.7	Summary	116
5	A System of Two Spin-1/2 Particles	120
5.1	The Basis States for a System of Two Spin-1/2 Particles	120
5.2	The Hyperfine Splitting of the Ground State of Hydrogen	122
5.3	The Addition of Angular Momenta for Two Spin-1/2 Particles	126
5.4	The Einstein-Podolsky-Rosen Paradox	131
5.5	A Nonquantum Model and the Bell Inequalities	134
5.6	Summary	143
6	Wave Mechanics in One Dimension	147
6.1	Position Eigenstates and the Wave Function	147
6.2	The Translation Operator	151
6.3	The Generator of Translations	153
6.4	The Momentum Operator in the Position Basis	156
6.5	Momentum Space	158
6.6	A Gaussian Wave Packet	160
6.7	The Heisenberg Uncertainty Principle	164
6.8	General Properties of Solutions to the Schrodinger Equation in Position Space	166
6.9	The Particle in a Box	171
6.10	Scattering in One Dimension	177
6.11	Summary	185
7	The One-Dimensional Harmonic Oscillator	194
7.1	The Importance of the Harmonic Oscillator	194
7.2	Operator Methods	196
7.3	An Example: Torsional Oscillations of the Ethylene Molecule	199
7.4	Matrix Elements of the Raising and Lowering Operators	201
7.5	Position-Space Wave Functions	202
7.6	The Zero-Point Energy	205
7.7	The Classical Limit	207
7.8	Time Dependence	208
7.9	Solving the Schrodinger Equation in Position Space	209
7.10	Inversion Symmetry and the Parity Operator	212
7.11	Summary	213
8	Path Integrals	216
8.1	The Multislit, Multiscreen Experiment	216
8.2	The Transition Amplitude	218
8.3	Evaluating the Transition Amplitude for Short Time Intervals	219
8.4	The Path Integral	221
8.5	Evaluation of the Path Integral for a Free Particle	224
8.6	Why Some Particles Follow the Path of Least Action	226
8.7	Quantum Interference Due to Gravity	231
8.8	Summary	233
9	Translational and Rotational Symmetry in the Two-Body Problem	237
9.1	The Elements of Wave Mechanics in Three Dimensions	237
9.2	Translational Invariance and Conservation of Linear Momentum	241
9.3	Relative and Center-of-Mass Coordinates	244
9.4	Estimating Ground-State Energies Using the Uncertainty Principle	246
9.5	Rotational Invariance and Conservation of Angular Momentum	248
9.6	A Complete Set of Commuting Observables	250
9.7	Vibrations and Rotations of a Diatomic Molecule	254
9.8	Position-Space Representations of L in Spherical Coordinates	260
9.9	Orbital Angular Momentum Eigenfunctions	263
9.10	Summary	268
10	Bound States of Central Potentials	274
10.1	The Behavior of the Radial Wave Function Near the Origin	274
10.2	The Coulomb Potential and the Hydrogen Atom	277
10.3	The Finite Spherical Well and the Deuteron	288
10.4	The Infinite Spherical Well	292
10.5	The Three-Dimensional Isotropic Harmonic Oscillator	296
10.6	Conclusion	302
11	Time-Independent Perturbations	306
11.1	Nondegenerate Perturbation Theory	306
11.2	An Example Involving the One-Dimensional Harmonic Oscillator	311
11.3	Degenerate Perturbation Theory	314
11.4	The Stark Effect in Hydrogen	316
11.5	The Ammonia Molecule in an External Electric Field Revisited	319
11.6	Relativistic Perturbations to the Hydrogen Atom	322
11.7	The Energy Levels of Hydrogen, Including Fine Structure, the Lamb Shift, and Hyperfine Splitting	331
11.8	The Zeeman Effect in Hydrogen	334
11.9	Summary	335
12	Identical Particles	341
12.1	Indistinguishable Particles in Quantum Mechanics	341
12.2	The Helium Atom	345
12.3	Multielectron Atoms and the Periodic Table	355
12.4	Covalent Bonding	360
12.5	Conclusion	366
13	Scattering	368
13.1	The Asymptotic Wave Function and the Differential Cross Section	368
13.2	The Born Approximation	375
13.3	An Example of the Born Approximation: The Yukawa Potential	379
13.4	The Partial Wave Expansion	381
13.5	Examples of Phase-Shift Analysis	385
13.6	Summary	393
14	Photons and Atoms	399
14.1	The Aharonov-Bohm Effect	399
14.2	The Hamiltonian for the Electromagnetic Field	404
14.3	Quantizing the Radiation Field	409
14.4	The Properties of Photons	410
14.5	The Hamiltonian of the Atom and the Electromagnetic Field	414
14.6	Time-Dependent Perturbation Theory	417
14.7	Fermi's Golden Rule	425
14.8	Spontaneous Emission	430
14.9	Higher-Order Processes and Feynman Diagrams	437
	Appendixes
A	Electromagnetic Units	444
B	The Addition of Angular Momenta	449
C	Dirac Delta Functions	453
D	Gaussian Integrals	457
E	The Lagrangian for a Charge q in a Magnetic Field	460
F	Values of Physical Constants	463
G	Answers to Selected Problems	465
	Index	467