Classical Dynamics and Its Quantum Analogues - Park, David

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Résumé :
A text in the classical dynamics of particles, rigid bodies, and continuous systems and corresponding aspects of quantum mechanics, emphasizing the connections and continuity between these two theories. Together with traditional topics it treats such matters as chaotic nonlinear dynamics and the difference between classical and quantum theories of continuous fields....

Sommaire:
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 Connectionswith Quantum Mechanics.- 7.5 Heisenberg's Quantum Mechanics.- 7.6 Matter Waves.- 7.7 Schr?dinger'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 M?ssbauer Effect.- 10.10 Classical and Quantum Descriptions of Nature.- References.- Notation.