Stern–Gerlach experiment 196
•
Spin-one systems 200
•
The classical limit 201
7.5
Addition of angular momenta
205
•
Case of two spin-half systems 210
•
Case of spin one and
spin half 212
•
The classical limit 213
⊲
Problems 214
8
Hydrogen
220
8.1
Gross structure of hydrogen
221
•
Emission-line spectra 226
•
Radial eigenfunctions 226
•
Shielding 231
•
Expectation values for
r
−
k
234

Contents
vii
8.2
Fine structure and beyond
235
•
Spin-orbit coupling 236
•
Hyperfine structure 241
⊲
Problems 243
9
Perturbation theory
246
9.1
Time-independent perturbations
247
•
Quadratic Stark effect 249
•
Linear Stark effect and
degenerate perturbation theory 250
•
Effect of an ex-
ternal magnetic field 253
⊲
Paschen–Back effect 255
⊲
Zeeman effect 255
9.2
Variational principle
258
9.3
Time-dependent perturbation theory
260
•
Fermi golden rule 261
•
Radiative transition rates 262
•
Selection rules 267
⊲
Problems 269
10 Helium and the periodic table
273
10.1 Identical particles
273
⊲
Generalisation to the case of
N
identical particles 275
•
Pauli exclusion principle 275
10.2 Gross structure of helium
277
•
Gross structure from perturbation theory 278
•
Application of the variational principle to he-
lium 280
•
Excited states of helium 281
•
Electronic configurations and spectroscopic terms 285
⊲
Spectrum of helium 286
10.3 The periodic table
286
•
From lithium to argon 286
•
The fourth and fifth peri-
ods 291
⊲
Problems 293
11 Adiabatic principle
295
11.1 Derivation of the adiabatic principle
296
11.2 Application to kinetic theory
298
11.3 Application to thermodynamics
301
11.4 The compressibility of condensed matter
303
11.5 Covalent bonding
304
•
A toy model of a covalent bond 305
•
Molecular dynam-
ics 307
•
Dissociation of molecules 308
11.6 The WKBJ approximation
309
⊲
Problems 310
12 Scattering Theory
313
12.1 The scattering operator
314
•
Perturbative treatment of the scattering operator 316
12.2 The S-matrix
318
•
The
i
ǫ
prescription 319
•
Expanding the S-matrix 321
•
The scattering amplitude 324
12.3 Cross-sections and scattering experiments
326
•
The optical theorem 330
12.4 Scattering electrons off hydrogen
332
12.5 Partial wave expansions
334
•
Scattering at low energy 339
12.6 Resonances
341
•
Breit–Wigner resonances 344
•
Radioactive decay 345
⊲
Problems 347

viii
Contents
Appendices
A
Cartesian tensors
349
B
Fourier series and transforms
351
C
Operators in classical statistical mechanics
353
D
Lorentz covariant equations
356
E
Thomas precession
358
F
Matrix elements for a dipole-dipole interaction
361
G
Selection rule for
j
363
H
Restrictions on scattering potentials
364
Index
365

Preface
This book grew out of classes given for many years to the second-year un-
dergraduates of Merton College, Oxford.
The University lectures that the
students were attending in parallel were restricted to the wave-mechanical
methods introduced by Schr¨odinger, with a very strong emphasis on the
time-independent Schr¨odinger equation. The classes had two main aims: to
introduce more wide-ranging concepts associated especially with Dirac and

#### You've reached the end of your free preview.

Want to read all 277 pages?

- Spring '15
- Unknow
- Physics, mechanics, The Land, probability amplitudes