Classical Dynamics and Its Quantum Analogues
2nd Edition
Published on 28. June 1990
Book
Hardback
IX, 333 pages
978-3-540-51398-8 (ISBN)
Description
The short Heroic Age of physics that started in 1925 was one of the rare occasions when a deep consideration of the question: What does physics really say? was necessary in carrying out numerical calculations. In many parts of microphysics the calculations have now become relatively straightforward if not easy, but most physicists seem to agree that some questions of principle remain to be resolved, even if they do not think it is very important to do so. This situation has affected the way people think and write about quantum mechanics, a gingerly approach to fundamentals and a tendency to emphasize what fifty years ago was new in the new theory at the expense of continuity with what came before it. Nowadays those who look into the subject are more likely to be struck by unexpected similarities between quantum and classical mechanics than by dramatic contrasts they had been led to expect. It is often said that the hardest part of understanding quantum mechanics is to understand that there is nothing to understand; all the same, to think quantum mechanically it helps to have firm mental connections with classical physics and to know exactly what these connections do and do not imply. This book originated more than a decade ago as informal lecture notes [OP, prepared for use in a course taught from time to time to advanced undergraduates at Williams College.
More details
Edition
2nd enlarged and updated ed.
Language
English
Place of publication
Heidelberg
Germany
Publishing group
Springer Berlin
Target group
College/higher education
Edition type
Revised edition
Illustrations
biography
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
670 gr
ISBN-13
978-3-540-51398-8 (9783540513988)
DOI
10.1007/978-3-642-74922-3
Schweitzer Classification
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Classical Dynamics and Its Quantum Analogues
E-Book
12/2012
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Springer
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Classical Dynamics and Its Quantum Analogues
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Previous edition
D. Park | David Allen Park
Classical Dynamics and Its Quantum Analogues
Book
11/1979
Springer
€66.95
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Content
1. Rays of Light.- 1.1 Waves, Rays, and Orbits.- 1.2 Phase Velocity and Group Velocity.- 1.3 Dynamics of a Wave Packet.- 1.4 Fermat's Principle of Least Time.- 1.5 Interlude on the Calculus of Variations.- 1.6 Optics in a Gravitational Field.- 2. Orbits of Particles.- 2.1 Ehrenfest's Theorems.- 2.2 Oscillators and Pendulums.- 2.3 Interlude on Elliptic Functions.- 2.4 Driven Oscillators.- 2.5 A Driven Anharmonic Oscillator.- 2.6 Quantized Oscillators.- 2.7 Coherent States.- 3. Lagrangian Dynamics.- 3.1 Lagrange's Equations.- 3.2 The Double Pendulum.- 3.3 Planets and Atoms.- 3.4 Orbital Oscillations and Stability.- 3.5 Orbital Motion: Vectorial Integrals and Hyperbolic Orbits.- 3.6 Other Forces.- 3.7 Bohr Orbits and Quantum Mechanics: Degeneracy.- 3.8 The Principle of Maupertuis and Its Practical Utility.- 4. N-Particle Systems.- 4.1 Center-of-Mass Theorems.- 4.2 Two-Particle Systems.- 4.3 Vibrating Systems.- 4.4 Coupled Oscillators.- 4.5 The Virial Theorem.- 4.6 Hydrodynamics.- 5. Hamiltonian Dynamics.- 5.1 The Canonical Equations.- 5.2 Magnetic Forces.- 5.3 Canonical Transformations.- 5.4 Infinitesimal Transformations.- 5.5 Generating Finite Transformations from Infinitesimal Ones.- 5.6 Deduction of New Integrals.- 5.7 Commutators and Poisson Brackets.- 5.8 Gauge Invariance.- 6. The Hamilton-Jacobi Theory.- 6.1 The Hamilton-Jacobi Equation.- 6.2 Step-by-Step Integration of the Hamilton-Jacobi Equation.- 6.3 Interlude on Planetary Motion in General Relativity.- 6.4 Jacobi's Generalization.- 6.5 Orbits and Integrals.- 6.6 "Chaos".- 6.7 Coordinate Systems.- 6.8 Curvilinear Coordinates.- 6.9 Interlude on Classical Optics.- 7. Action and Phase.- 7.1 The Old Quantum Theory.- 7.2 Hydrogen Atom in the Old Quantum Theory.- 7.3 The Adiabatic Theorem.- 7.4 Connections with Quantum Mechanics.- 7.5 Heisenberg's Quantum Mechanics.- 7.6 Matter Waves.- 7.7 Schrödinger's "Derivation".- 7.8 Construction of a Wave Function.- 7.9 Phase Shifts in Dynamics.- 8. Theory of Perturbations.- 8.1 Secular and Periodic Perturbations.- 8.2 Perturbations in Quantum Mechanics.- 8.3 Adiabatic Perturbations.- 8.4 Degenerate States.- 8.5 Quantum Perturbation Theory for Positive-Energy States.- 8.6 Action and Angle Variables.- 8.7 Canonical Perturbation Theory.- 8.8 Newtonian Precession.- 9. The Motion of a Rigid Body.- 9.1 Angular Velocity and Momentum.- 9.2 The Inertia Tensor.- 9.3 Dynamics in a Rotating Coordinate System.- 9.4 Euler's Equations.- 9.5 The Precession of the Equinoxes.- 9.6 Quantum Mechanics of a Rigid Body.- 9.7 Spinors.- 9.8 Particles with Spin.- 10. Continuous Systems.- 10.1 Stretched Strings.- 10.2 Four Modes of Description.- 10.3 Example: A Plucked String.- 10.4 Practical Use of Variation Principles.- 10.5 More Than One Dimension.- 10.6 Waves in Space.- 10.7 The Matter Field.- 10.8 Quantized Fields.- 10.9 The Mössbauer Effect.- 10.10 Classical and Quantum Descriptions of Nature.- References.- Notation.