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Path integrals in quantum mechanics, statistics, polymer physics, and financial markets /
"This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutio...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2009.
|
| Edición: | 5th ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Kleinert, Hagen, |e author. | |
| 245 | 1 | 0 | |a Path integrals in quantum mechanics, statistics, polymer physics, and financial markets / |c Hagen Kleinert. |
| 250 | |a 5th ed. | ||
| 260 | |a New Jersey : |b World Scientific, |c ©2009. | ||
| 300 | |a 1 online resource (xliii, 1579 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a "This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r[superscript 2] potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations." "In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions." "The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals." "Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory now also applies to small orders." "Special attention is devoted to path integrals with -- | ||
| 520 | |a Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface to Fourth Edition; Preface; Preface to Third Edition; Preface to Second Edition; Preface to First Edition; Contents; List of Figures; List of Tables; 1 Fundamentals; 1.1 Classical Mechanics; 1.2 Relati vistic Mechanics in Curved Spacetime; l.3 Quantum Mechanics; 1.3.1 Bragg Reflections and Interference; 1.3.2 Matter Waves; 1.3.3 SchrOdinger Equation; 1.3.4 Particle Current Conservation; 1.4 Dirac's Bra-Ket Formalism.; 1.4.1 Basis Transformations; 1.4.2 Bracket Notation; 1.4.3 Continuum Limit; 1.4.4 Generalized Functions; 1.4.5 SchrOdinger Equation in Dirac Notation | |
| 505 | 8 | |a 1.4.6 Momentum States1.4.7 Incompleteness and Poisson's Summation Formula; 1.5 Obscrvables; 1.5.1 Uncertainty Relation.; 1.5.2 Density Matrix and Wigner Function.; 1.5.3 Generalization to Many Particles; 1.6 Time Evolution Operator; l.7 Properties of the Time Evolution Operator; 1.8 Heisenberg Picture of Quantum Mechanics; l.9 Interaction Picture and Perturbation Expansion; 1.10 Time Evolution Amplitude; 1.11 Fixed-Energy Amplitude; 1.12 Free-Particle Amplitudes.; 1.13 Quantum Mechanics of General Lagrangian Systems.; 1.14 Particle on the Surface of a Sphere; 1.15 Spinning Top | |
| 505 | 8 | |a 1.16 Scattering1. 16.1 Scattering Matrix; 1.16.2 Cross Section; 1.16.3 Born Approximation; 1. 16.4 Partial Wave Expansion and Eikonal Approximation; 1. 16.5 Scattering Amplitude from Time Evolution Amplitude; 1. 16.6 Lippmann-Schwinger Equation; 1.17 Classical and Quantum Statistics; 1. 17.1 Canonical Ensemble.; 1. 17.2 Grand-Canonical Ensemble; 1.18 Density of States and Ttacelog; Appendix l A Simple Time Evolution Operator.; Appendix I B Convergence of the Fresnel Integral; Appendix l C The Asymmetric Top; Notes and References.; 2 Path Integrals -- Elementary Properties and Simple Solutions | |
| 505 | 8 | |a 2.1 Path Integral Representation of Time Evolution Amplitudcs2.1.1 Sliced Time Evolution Amplitude.; 2.1.2 Zero-Hamiltonian Path Integral.; 2.1.3 SchrOdinger Equation for Time Evolution Amplitude; 2.1.4 Convergence of of the Time-Sliced Evolution Amplitude; 2.1.5 Time Evolution Amplitude in Momentum Space.; 2.1.6 Quantum-Mechanical Partition Function.; 2.1.7 Feynman's Configurat ion Space Pat h Integral; 2.2 Exact Solution for the Frec Particle; 2.2. 1 Direct Solution; 2.2.2 Fluctuations around the Classical Path; 2.2.3 Fluctuation Factor | |
| 505 | 8 | |a 2.2.4 Finite Slicing Properties of Free-Particle Amplitude.2.3 Exact Solution for Harmonic Oscillator; 2.3. 1 Fluctuations around the Classical Path.; 2.3.2 Fluctuation Factor; 2.3.3 The i7]-Prescription and Maslov-Morse Index; 2.3.4 Continuum Limit.; 2.3.5 Useful Fluctuation Formulas.; 2.3.6 Oscillator Amplitude on Finite Time Lattice; 2.4 Gelfand-Yaglom Formula.; 2.4. 1 Recursive Calculation of Fluctuation Detcrminant.; 2.4.2 Examples; 2.4.3 Calculation on Unsliced Time Axis; 2.4.4 D'Alembert's Construction; 2.4 .5 Another Simple Formula.; 2.4.6 Generalization t o D Dimensions | |
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| 650 | 0 | |a Path integrals. | |
| 650 | 0 | |a Quantum theory. | |
| 650 | 0 | |a Statistical physics. | |
| 650 | 0 | |a Polymers. | |
| 650 | 6 | |a Intégrales de chemin. | |
| 650 | 6 | |a Théorie quantique. | |
| 650 | 6 | |a Physique statistique. | |
| 650 | 6 | |a Polymères. | |
| 650 | 7 | |a polymers. |2 aat | |
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| 776 | 0 | 8 | |i Print version: |a Kleinert, Hagen. |t Path integrals in quantum mechanics, statistics, polymer physics, and financial markets. |b 5th ed. |d New Jersey : World Scientific, ©2009 |z 9789814273558 |w (DLC) 2009278813 |w (OCoLC)465681898 |
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