Chaos in Classical and Quantum MechanicsDescribes 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. |
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Índice
LXXVIII | 188 |
LXXIX | 190 |
LXXX | 194 |
LXXXI | 196 |
LXXXII | 198 |
LXXXIII | 200 |
LXXXIV | 202 |
LXXXV | 204 |
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XLVII | 106 |
XLVIII | 109 |
XLIX | 111 |
L | 116 |
LI | 118 |
LII | 120 |
LIII | 125 |
LIV | 129 |
LV | 132 |
LVI | 135 |
LVII | 138 |
LVIII | 142 |
LIX | 143 |
LX | 145 |
LXI | 147 |
LXII | 149 |
LXIII | 151 |
LXIV | 154 |
LXV | 156 |
LXVI | 159 |
LXVII | 161 |
LXVIII | 164 |
LXIX | 168 |
LXX | 171 |
LXXI | 173 |
LXXII | 174 |
LXXIII | 176 |
LXXIV | 178 |
LXXV | 180 |
LXXVI | 184 |
LXXVII | 186 |
LXXXVI | 207 |
LXXXVII | 208 |
LXXXVIII | 211 |
LXXXIX | 215 |
XC | 220 |
XCI | 224 |
XCII | 227 |
XCIII | 231 |
XCIV | 232 |
XCV | 233 |
XCVI | 238 |
XCVII | 241 |
XCVIII | 247 |
XCIX | 249 |
C | 254 |
CI | 255 |
CII | 257 |
CIII | 261 |
CIV | 263 |
CV | 266 |
CVI | 270 |
CVII | 273 |
CVIII | 275 |
CIX | 278 |
CX | 282 |
CXI | 283 |
CXII | 285 |
CXIII | 287 |
CXIV | 291 |
CXV | 295 |
CXVI | 298 |
CXVII | 301 |
CXVIII | 305 |
CXIX | 307 |
CXX | 312 |
CXXI | 314 |
CXXII | 317 |
CXXIII | 322 |
CXXIV | 323 |
CXXV | 325 |
CXXVI | 326 |
CXXVII | 329 |
CXXVIII | 332 |
CXXIX | 336 |
CXXX | 340 |
CXXXI | 341 |
CXXXII | 345 |
CXXXIII | 348 |
CXXXIV | 354 |
CXXXV | 358 |
CXXXVI | 363 |
CXXXVII | 369 |
CXXXVIII | 374 |
CXXXIX | 377 |
CXL | 379 |
CXLI | 383 |
CXLII | 384 |
CXLIII | 389 |
CXLIV | 393 |
CXLV | 395 |
CXLVI | 398 |
CXLVII | 402 |
CXLVIII | 407 |
CXLIX | 410 |
CL | 427 |
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Palavras e frases frequentes
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 yields
Passagens conhecidas
Página 135 - Hamiltonian perturbations, most non-resonant invariant tori do not vanish, but are only slightly deformed, so that in the phase space of the perturbed system there...
Página 427 - YAFET, Y., KEYES, RW, and ADAMS, EN, 1956, J. Phys. Chem. Solids., 1, 137.
Página 417 - In Ghil, M., Benzi, R. and Parisi, G. (eds); Turbulence and predictability in geophysical fluid dynamics and climate dynamics.
Página 309 - Zeta function is probably the most challenging and mysterious object of modern mathematics, in spite of its utter simplicity. . . The main interest comes from trying to improve the Prime Number Theorem, ie getting better estimates for the distribution of the prime numbers. The secret to the success is assumed to lie in proving a conjecture which Riemann stated in 1859 without much fanfare, and whose proof has since then become the single most desirable achievement for a mathematician.
Página viii - ... and quantum, has become a growth industry in the last decade. A newcomer to this flourishing field must get acquainted with some unfamiliar concepts and get rid of some cherished assumptions. The change in orientation is necessary because physicists have finally realized that most dynamical systems do not follow simple, regular, and predictable patterns, but run along a seemingly random, yet well-defined, trajectory. The generally accepted name for this phenomenon is chaos, a term that accurately...
Página ii - Advisors G. Ezra M. Gutzwiller D. Holm DD Joseph PS Krishnaprasad J. Murray M. Schultz K. Sreenivasan S. Winograd Springer New York Berlin Heidelberg Barcelona Hong Kong London Milan Paris Tokyo 1 . Gutzwiller: Chaos in Classical and Quantum Mechanics 2.
Página 196 - Quantum mechanics has liberated us from the scourge of classical chaos, and we will find that the symptoms of chaos are hard to pin down in this new environment.
Página 144 - While the idea of an entropy is of great help in understanding classical mechanical systems, nobody has been able to find its analog in quantum mechanics; therein lies the great unresolved mystery of quantum chaos.
Página 78 - The main ideas come out clearly when studying a particle moving in a plane under the influence of a potential V(r) that depends only on the distance r from the origin. Einstein (1917) gave this example in his paper on quantization conditions, which has inspired many researchers ever since it was "discovered
Página 239 - A<? are Gaussians both in position and in momentum space. Such functions are convenient as a basis from which to build many-particle correlated wave functions for complicated atoms and molecules, because overlap integrals and interaction matrix elements can be worked out algebraically.
Referências a este livro
Nonlinear Differential Equations and Dynamical Systems Ferdinand Verhulst Pré-visualização limitada - 2006 |
Informação bibliográfica
| Título | Chaos in Classical and Quantum Mechanics Volume 1 de Interdisciplinary Applied Mathematics |
| Autor | Martin C. Gutzwiller |
| Edição | ilustrada, reimpressão |
| Editora | Springer Science & Business Media, 1991 |
| ISBN | 0387971734, 9780387971735 |
| Número de páginas | 432 páginas |
| Exportar citação | BiBTeX EndNote RefMan |