Chaos in Classical and Quantum MechanicsSpringer Science & Business Media, 01.08.1991 - 432 Seiten 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. |
Inhalt
Introduction | 1 |
The Mechanics of Hamilton and Jacobi | 19 |
Integrable Systems | 30 |
MoonEarthSun | 45 |
Three Methods of Solution | 58 |
Periodic Orbits | 75 |
The Surface of Section | 87 |
Models of the Galaxy and of Small Molecules | 99 |
The New World of Quantum Mechanics | 194 |
The Quantization of Integrable Systems | 207 |
Wave Functions in Classically Chaotic Systems | 231 |
The Energy Spectrum of a Classically Chaotic System | 254 |
The Trace Formula | 282 |
The Diamagnetic Kepler Problem | 322 |
Motion on a Surface of Constant Negative Curvature | 340 |
Scattering Problems Coding and Multifractal Invariant | 383 |
Soft Chaos and the KAM Theorem | 116 |
Entropy and Other Measures of Chaos | 142 |
The Anisotropic Kepler Problem | 156 |
The Transition from Classical to Quantum Mechanics | 173 |
References | 410 |
| 427 | |
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Häufige Begriffe und Wortgruppen
action angle angular atom becomes binary calculated called carried chaos chaotic chapter classical close complete condition constant construction continuous coordinates corresponding defined degrees of freedom depends derivatives determinant direction discussed distance dynamical system energy energy levels equation example expression factor field Figure fixed formula frequency function given gives Hamiltonian idea increases initial integral intersections interval invariant Kepler length limit lines mass mathematical measure method momentum motion natural obtained original parameters particle particular periodic orbit perturbation phase space Phys physics plane position potential problem quantum mechanics ratio reader relation requires resonance respect result scattering sequence shows side simple singular spectrum square starting surface surface of section takes tori torus trace formula trajectory transformation variables wave function whole yields
Beliebte Passagen
Verweise auf dieses Buch
Nonlinear Differential Equations and Dynamical Systems Ferdinand Verhulst Eingeschränkte Leseprobe - 2006 |