A Primer of Analytical Mechanics
In turn, the book’s closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum...
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2018, 2018
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| Edition: | 1st ed. 2018 |
| Series: | UNITEXT for Physics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preface
- 1 Difficulties of Cartesian Newtonian Mechanics
- 1.1 Constraint forces
- 1.2 Non-inertial frames and fictitious forces
- 2 Lagrange equations
- 2.1 Degrees of freedom and Lagrangian coordinates
- 2.2 Lagrangian form of Newton's equations
- 2.3 Lagrange equations
- 2.4 Lagrange equations at work. Examples
- 2.5 Generalized potential
- 2.6 Larmor theorem
- 2.7 Physical meaning of Lagrange equations; conjugate momenta
- 2.8 Cyclic variables, symmetries and conserved conjugate momenta
- 2.9 Non-uniqueness of the Lagrangian
- 3 Hamilton equations
- 3.1 Energy conservation
- 3.2 Hamilton equations
- 3.3 Coordinate transformations and Hamilton equations
- 3.4 Canonical transformations
- 4 Poisson brackets and canonical structure
- 4.1 Constants of motion identified by
- Poisson brackets
- 4.2 General properties of Poisson brackets
- 4.3 Canonical structure
- 4.4 Invariance of Poisson brackets under canonical transformations
- 5 Generation of canonical transformations
- 5.1 Alternative characterization of canonical transformations
- 5.2 Extended canonical transformations
- 5.3 Generators of continuous groups of canonical transformations
- 5.4 Symmetries and conservation laws. Noether theorem
- 6 Small oscillations
- 6.1 Equilibrium configurations. Stability
- 6.2 Small oscillations
- 7 The common Poisson algebra of classical and quantum mechanics
- 7.1 Dirac Poisson algebra
- 7.2 A common Poisson algebra of classical and quantum mechanics
- Index