Chaos in classical and quantum mechanics
Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field
Interdisciplinary applied mathematics, v. 1, volume 1
1 online resource (xiii, 432 pages) : illustrations
9781461209836, 9781461269700, 1461209838, 1461269709
883391909
1. The mechanics of Lagrange
2. The mechanics of Hamilton and Jacobi
3. Integrable systems
4. The three-body problem : moon-earth-sun
5. Three methods of solution
6. Periodic orbits
7. The surface of section
8. Models of the galazy and of small molecules
9. Soft chaos and the KAM theorem
10. Entropy and other measures of chaos
11. The anisotropic Kepler problem
12. The transition from classical to quantum mechanics
13. The new world of quantum mechanics
14. The quantization of integrable systems
15. Wave functions in classically chaotic systems
16. The energy spectrum of a classically chaotic system
17. The trace formula
18. The diamagnetic Kepler problem
19. Motion on a surface of constant negative curvature
20. Scattering problems, coding, and multifractal invariant measures
English