3 The formalism of quantum mechanics: motivation

Chapters in this book

1. Frontmatter I
2. Preface VII
3. Contents XIII
4. 1 The classical harmonic oscillator 1
5. 2 Lagrangian and Hamiltonian mechanics 9
6. 3 The formalism of quantum mechanics: motivation 67
7. 4 Physical background 79
8. 5 Synopsis of self-adjoint operators, spectral theory and Stone’s theorem 129
9. 6 The postulates of quantum mechanics 189
10. 7 Canonical quantization 231
11. 8 Path integral quantization 311
12. 9 Sketches of some rigorous results 339
13. 10 Fermionic and supersymmetric harmonic oscillators 391
14. A Gaussian integrals 455
15. B Morse lemma 465
16. C Stationary phase approximation 473
17. D Tangent and cotangent bundles 481
18. E Poisson and wave equations 483
19. F Carathéodory procedure 485
20. G Schwartz space, Fourier transform, distributions and Sobolev spaces 487
21. H Stieltjes integrals 511
22. I Unitary representations and Schur’s lemma 517
23. J Semigroups of operators 521
24. K Hilbert space tensor products 529
25. Bibliography 531
26. Index 543