Binney J. The physics of quantum mechanics (Oxford, 2014). - ОГЛАВЛЕНИЕ / CONTENTS

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ОбложкаBinney J. The physics of quantum mechanics / J.Binney, D.Skinner. - Oxford: Oxford university press, 2014. - xiii, 392 p.: ill. - Ind.: p.383-392. - ISBN 978-0-19-968857-9
 

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Оглавление / Contents
 
Preface ....................................................... XII
1  Introduction ................................................. 1
   1.1  Origins ................................................. 2
   1.2  Measurements ............................................ 6
        Measurement involves disturbance ........................ 7
        Heisenberg microscope ................................... 7
        Ideal measurements ...................................... 8
        Summary ................................................ 10
   1.3  Probability amplitudes ................................. 11
        Two-slit interference .................................. 12
   1.4  Quantum states ......................................... 14
        Observables ............................................ 14
        Complete sets of amplitudes ............................ 14
        Vector spaces and their duals .......................... 16
        The energy representation .............................. 19
        Polarisation of photons ................................ 20
   1.5  Summary ................................................ 23
        Problems ............................................... 24
2  Operators, measurement and time evolution ................... 25
   2.1  Operators .............................................. 25
        Functions of operators ................................. 29
        Commutators ............................................ 29
   2.2  Evolution in time ...................................... 31
        Evolution of expectation values ........................ 32
   2.3  The position representation ............................ 34
        Hamiltonian of a particle .............................. 37
        Wavefunction for well-defined momentum ................. 38
        The uncertainty principle .............................. 39
        Dynamics of a free particle ............................ 41
        Back to two-slit interference .......................... 43
        Generalisation to three dimensions ..................... 44
        Probability current .................................... 45
        The virial theorem ..................................... 46
   2.4  Summary ................................................ 47
        Problems ............................................... 48
3  Oscillators ................................................. 52
   3.1  Stationary states of a harmonic oscillator ............. 52
   3.2  Dynamics of oscillators ................................ 56
        Anharmonic oscillators ................................. 58
        Problems ............................................... 61
4  Transformations and observables ............................. 66
   4.1  Transforming kets ...................................... 66
        Translating kets ....................................... 67
        Continuous transformations and generators .............. 69
        The rotation operator .................................. 71
        Discrete transformations ............................... 72
        The parity operator .................................... 72
        Mirror operators ....................................... 73
   4.2  Transformations of operators ........................... 74
        The parity operator .................................... 76
        Mirror operators ....................................... 78
   4.3  Symmetries and conservation laws ....................... 79
   4.4  The Heisenberg picture ................................. 81
   4.5  What is the essence of quantum mechanics? .............. 83
        Problems ............................................... 85
5  Motion in step potentials ................................... 88
   5.1  Square potential well .................................. 88
        Limiting cases ......................................... 91
        Infinitely deep well ................................... 91
        Infinitely narrow well ................................. 92
   5.2  A pair of square wells ................................. 93
        Ammonia ................................................ 96
        The ammonia maser ...................................... 97
   5.3  Scattering of free particles ........................... 99
        The scattering cross-section .......................... 102
        Tunnelling through a potential barrier ................ 103
        Scattering by a classically allowed region ............ 104
        Resonant scattering ................................... 106
        The Breit-Wigner cross-section ........................ 109
   5.4  How applicable are our results? ....................... 113
   5.5  Summary ............................................... 115
        Problems .............................................. 117
6  Composite systems .......................................... 123
   6.1  Composite systems ..................................... 124
        Collapse of the wavefunction .......................... 128
        Operators for composite systems ....................... 129
        Development of entanglement ........................... 131
        Einstein-Podolski-Rosen experiment .................... 132
        Bell's inequality ..................................... 134
   6.2  Quantum computing ..................................... 137
   6.3  The density operator .................................. 144
        Reduced density operators ............................. 148
        Shannon entropy ....................................... 151
   6.4  Thermodynamics ........................................ 154
   6.5  Measurement ........................................... 158
        Problems .............................................. 162
7  Angular momentum ........................................... 167
   7.1  Eigenvalues of Jz and J2 .............................. 168
        Rotation spectra of diatomic molecules ................ 171
   7.2  Spin and orbital angular momentum ..................... 174
        Orbital angular momentum .............................. 174
        L as the generator of circular translations ........... 176
        Spectra of and L2 and Lz .............................. 177
        Spin angular momentum ................................. 177
   7.3  Physics of spin ....................................... 180
        Spin-half matrices .................................... 181
        Spin-one matrices ..................................... 182
   7.4  Orbital angular-momentum eigenfunctions ............... 191
        The Stern-Gerlach experiment .......................... 183
        Stern-Gerlach experiment with spin-one atoms .......... 186
        Precession in a magnetic field ........................ 187
        The classical Umit .................................... 188
        Orbital angular momentum and parity ................... 196
        Orbital angular momentum and kinetic energy ........... 196
        Legendre polynomials .................................. 198
   7.5  Three-dimensional harmonic oscillator ................. 199
   7.6  Addition of anguleu momenta ........................... 205
        Case of two spin-half systems ......................... 209
        Case of spin-one and spin-half ........................ 211
        The classical limit ................................... 212
        Problems .............................................. 213
8  Hydrogen ................................................... 219
   8.1  Gross structure of hydrogen ........................... 220
        Emission-line spectra ................................. 226
        Radial eigenfunctions ................................. 226
        Shielding ............................................. 231
        Expectation values for r-k ............................ 234
   8.2  Fine structure and beyond ............................. 236
        Spin-orbit coupling ................................... 236
        Hyperfine structure ................................... 241
        Problems .............................................. 243
9  Motion in a magnetic field ................................. 247
   9.1  Hamiltonian for motion in a magnetic field ............ 248
        Classical equations of motion ......................... 248
   9.2  Gauge transformations ................................. 250
        Probability current ................................... 251
   9.3  Landau levels ......................................... 252
        Displacement of the gyrocentre ........................ 255
   9.4  Aharonov-Bohm effect .................................. 257
        Problems .............................................. 259
10 Perturbation theory ........................................ 262
   10.1 Time-independent perturbations ........................ 263
        Quadratic Stark effect ................................ 265
        Linear Stark effect and degenerate perturbation
        theory ................................................ 266
        Effect of an external magnetic field .................. 269
        Paschen-Back effect ................................... 271
        Zeeman effect ......................................... 271
   10.2 Variational principle ................................. 273
   10.3 Time-dependent perturbation theory .................... 275
        Fermi golden rule ..................................... 276
        Radiative transition rates ............................ 277
        Selection rules ....................................... 282
        Problems .............................................. 284
11 Helium and the periodic table .............................. 290
   11.1 Identical particles ................................... 290
        Generalisation to the case of N identical particles ... 291
        Pauli exclusion principle ............................. 292
        Electron pairs ........................................ 293
   11.2 Gross structure of helium ............................. 295
        Gross structure from perturbation theory .............. 296
        Application of the variational principle to helium .... 298
        Excited states of heUum ............................... 299
        Electronic configurations and spectroscopic terms ..... 302
        Spectrum of helium .................................... 303
   11.3 The periodic table .................................... 303
        From lithium to argon ................................. 303
        The fourth and fifth periods .......................... 308
        Problems .............................................. 309
12 Adiabatic principle ........................................ 312
   12.1 Derivation of the adiabatic principle ................. 313
   12.2 Application to kinetic theory ......................... 315
   12.3 Application to thermodynamics ......................... 317
   12.4 The compressibility of condensed matter ............... 318
   12.5 Covalent bonding ...................................... 320
        A model of a covalent bond ............................ 320
        Molecular dynamics .................................... 322
        Dissociation of molecules ............................. 323
   12.6 The WKBJ approximation ................................ 324
        Problems .............................................. 325
13 Scattering theory .......................................... 327
   13.1 The scattering operator ............................... 328
        Perturbative treatment of the scattering operator ..... 330
   13.2 The S-matrix .......................................... 332
        The ie prescription ................................... 332
        Expanding the S-matrix ................................ 334
        The scattering ampUtude ............................... 336
   13.3 Cross-sections and scattering experiments ............. 339
        The optical theorem ................................... 342
   13.4 Scattering electrons ofF hydrogen ..................... 344
   13.5 Partial wave expansions ............................... 346
        Scattering at low energy .............................. 351
   13.6 Resonant scattering ................................... 353
        Breit-Wigner resonances ............................... 356
        Radioactive decay ..................................... 356
        Problems .............................................. 358
Appendices
A  The laws of probability .................................... 361
В  Ceirtesian tensors ......................................... 363
С  Fourier series and transforms .............................. 365
D  Operators in classical statistical mechanics ............... 367
E  Lie groups and Lie algebras ................................ 369
F  The hidden symmetry of hydrogen ............................ 370
G  Lorentz covariant equations ................................ 372
H  Thomas precession .......................................... 376
I  Matrix elements for a dipole-dipole interaction ............ 378
J  Selection rule for j ....................................... 380
К  Restrictions on scattering potentials ...................... 381

Index ......................................................... 383


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