Contents

Preface ix

Preface to the English Edition xi

§1. The algebra of observables in classical mechanics 1

§2. States 6

§3. Liouville’s theorem, and two pictures of motion in

classical mechanics 13

§4. Physical bases of quantum mechanics 15

§5. A finite-dimensional model of quantum mechanics 27

§6. States in quantum mechanics 32

§7. Heisenberg uncertainty relations 36

§8. Physical meaning of the eigenvalues and eigenvectors of

observables 39

§9. Two pictures of motion in quantum mechanics. The

Schr¨ odinger equation. Stationary states 44

§10. Quantum mechanics of real systems. The Heisenberg

commutation relations 49

§11. Coordinate and momentum representations 54

§12. “Eigenfunctions” of the operators Q and P 60

§13. The energy, the angular momentum, and other examples

of observables 63

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