Contents
Preface xiii
Part 1. Foundations
Chapter 1. Classical Mechanics 3
§1. Lagrangian Mechanics 4
1.1. Generalized coordinates 4
1.2. The principle of the least action 4
1.3. Examples of Lagrangian systems 8
1.4. Symmetries and Noether’s theorem 15
1.5. One-dimensional motion 20
1.6. The motion in a central field and the Kepler problem 22
1.7. Legendre transform 26
§2. Hamiltonian Mechanics 31
2.1. Hamilton’s equations 31
2.2. The action functional in the phase space 33
2.3. The action as a function of coordinates 35
2.4. Classical observables and Poisson bracket 38
2.5. Canonical transformations and generating functions 39
2.6. Symplectic manifolds 42
2.7. Poisson manifolds 51
2.8. Hamilton’s and Liouville’s representations 56
§3. Notes and references 60
Chapter 2. Basic Principles of Quantum Mechanics 63
§1. Observables, states, and dynamics 65
1.1. Mathematical formulation 66
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