1 Ideas and principles 1
Quantum world 1
Probability waves 3
Physical operators 6
Noncommutative physics 10
Moment of momentum 14
Perturbation theory 19
Factorization 21
Oscillator 23
Quantum numbers 27
2 Physics of the electron 31
Hydrogen atom 31
Bohr's formula 33
Matrix elements 37
Dirac's equation 38
Relativistic invariance 43
Spin one-half 46
Pauli's theory 52
Elementary consequences 57
Useful deftnitions 61
Positrons 63
Fine structure 64
Solution according to factorization 68
Magnetic interaction 71
Landau levels 74
Anharmonicity 76
3 Theory of anharmonicity 79
Model Hamiltonian 79
Perturbation method 82
Inclusion of degenerate levels 86
Polynomial formalism 89
Ensemble of anharmonic oscillators 94
General equations 97
Physical interpretation 99
Rules for polynomials 101
Quantum functions 104
Other anharmonic models 106
Morse potential 107
Generalized Morse problem 110
4 Quantum fields 115
Creation and destruction operators 115
Free scalar field 120
Quantization of electromagnetic field 126
Fermi's ideology 128
Electron-positron Dirac field 133
Interaction picture 138
Solution according to perturbation theory 144
Normal product 147
Ultraviolet divergences 152
Regularization of interaction energy 152
5 Radiative corrections 159
Renormalization of mass 159
Anomalous magnetic moment of the electron 165
On the history of radiative corrections 172
Bethe's formula 173
Electromagnetic shift of atomic levels 177
Vacuum polarization 185
Renormalization of charge 192
Dirac's ideas and quantum field theory 193
Bibliography 197