| Dedication | p. v |
| Preface | p. vii |
| Introduction | p. 1 |
| Phenomenological Equations of Motion for Dissipative Systems | p. 5 |
| Frictional Forces Linear Velocity | p. 5 |
| Raleigh's Oscillator | p. 8 |
| One-Dimensional Motion and Bopp Transformation | p. 8 |
| The Classical Theory of Line Width | p. 11 |
| Frictional Forces Quadratic in Velocity | p. 12 |
| Non-Newtonian and Nonlocal Dissipative Forces | p. 13 |
| Lagrangian Formulations | p. 15 |
| Rayleigh and Lur'e Dissipative Functions | p. 15 |
| Inverse Problem of Analytical Dynamics | p. 20 |
| Some Examples of the Lagrangians for Dissipative Systems | p. 24 |
| Non-Uniqueness of the Lagrangian | p. 27 |
| Acceptable Lagrangians for Dissipative Systems | p. 30 |
| Hamiltonian Formulation | p. 33 |
| Inverse Problem for the Hamiltonian | p. 33 |
| Hamiltonians for Simple Dissipative Systems | p. 36 |
| Ostrogradsky's Method | p. 39 |
| Complex or Leaky Spring Constant | p. 42 |
| Dekker's Complex Coordinate Formulation | p. 42 |
| Hamiltonian Formulation of the Motion of a Particle with Variable Mass | p. 44 |
| Variable Mass Oscillator | p. 45 |
| Bateman's Damped-Amplified Harmonic Oscillators | p. 47 |
| Dissipative Forces Quadratic in Velocity | p. 48 |
| Resistive Forces Proportional to Arbitrary Powers of Velocity | p. 48 |
| Universal Lagrangian and Hamiltonian | p. 49 |
| Hamiltonian Formulation in Phase Space of N-Dimensions | p. 52 |
| Symmetric Phase Space Formulation of the Damped Harmonic Oscillator | p. 55 |
| Dynamical Systems Expressible as Linear Difference Equations | p. 57 |
| Hamilton-Jacobi Formulation | p. 63 |
| The Hamilton-Jacobi Equation for Linear Damping | p. 64 |
| Classical Action for an Oscillator with Leaky Spring Constant | p. 66 |
| More About the Hamilton-Jacobi Equation for the Damped Motion | p. 67 |
| Motion of a Charged Particle in an External Electromagnetic Field in the Presence of Damping | p. 71 |
| Noether and Non-Noether Symmetries and Conservation Laws | p. 77 |
| Non-Noether Symmetries and Conserved Quantities | p. 84 |
| Noether's Theorem for a Scalar Field | p. 86 |
| Dissipative Forces Derived from Many-Body Problems | p. 91 |
| The Schrodinger Chain | p. 91 |
| A Particle Coupled to a Chain | p. 93 |
| Dynamics of a Non-Uniform Chain | p. 94 |
| Mechanical System Coupled to a Heat Bath | p. 98 |
| Euclidean Lagrangian | p. 104 |
| A Particle Coupled to a Field | p. 107 |
| Harmonically Bound Radiating Electron | p. 107 |
| An Oscillator Coupled to a String of Finite Length | p. 109 |
| An Oscillator Coupled to an Infinite String | p. 112 |
| Damped Motion of the Central Particle | p. 117 |
| Diagonalization of the Hamiltonian | p. 117 |
| Classical Microscopic Models of Dissipation and Minimal Coupling Rule | p. 125 |
| Quantization of Dissipative Systems | p. 129 |
| Early Attempts to Quantize the Damped Oscillator | p. 129 |
| Yang-Feldman Method of Quantization | p. 136 |
| Heisenberg's Equations of Motion for Dekker's Formulation | p. 138 |
| Quantization of the Bateman Hamiltonian | p. 139 |
| Fermi's Nonlinear Equation for Quantized Radiation Reaction | p. 142 |
| Attempts to Quantize Systems with a Dissipative Force Quadratic in Velocity | p. 145 |
| Solution of the Wave Equation for Linear and Newtonian Damping Forces | p. 147 |
| The Classical Limit of the Schrodinger Equation with Velocity-Dependent Forces | p. 150 |
| Quadratic Damping as an Externally Applied Force | p. 151 |
| Motion in a Viscous Field of Force Proportional to an Arbitrary Power of Velocity | p. 153 |
| The Classical Limit and the Van Vleck Determinant | p. 154 |
| Quantization of Explicitly Time-Dependent Hamiltonian | p. 157 |
| Wave Equation for the Kanai-Caldirola Hamiltonian | p. 157 |
| Coherent States of a Damped Oscillator | p. 164 |
| Squeezed State of a Damped Harmonic Oscillator | p. 167 |
| Quantization of a System with Variable Mass | p. 169 |
| The Schrodinger-Langevin Equation for Linear Damping | p. 172 |
| An Extension of the Madelung Formulation | p. 175 |
| Quantization of a Modified Hamilton-Jacobi Equation for Damped Systems | p. 180 |
| Exactly Solvable Cases of the Schrodinger-Langevin Equation | p. 184 |
| Harmonically Bound Radiating Electron and the Schrodinger-Langevin Equation | p. 187 |
| Other Phenomenological Nonlinear Potentials for Dissipative Systems | p. 189 |
| Scattering in the Presence of Frictional Forces | p. 192 |
| Application of the Noether Theorem: Linear and Nonlinear Wave Equations for Dissipative Systems | p. 193 |
| Wave Equation for Impulsive Forces Acting at Certain Intervals | p. 196 |
| Classical Limit for the Time-Dependent Problems | p. 197 |
| Density Matrix and the Wigner Distribution Function | p. 201 |
| Classical Distribution Function for Nonconservative Motions | p. 201 |
| The Density Matrix | p. 205 |
| Phase Space Quantization of Dekker's Hamiltonian | p. 207 |
| Density Operator and the Fokker-Planck Equation | p. 209 |
| The Density Matrix Formulation of a Solvable Model | p. 213 |
| Wigner Distribution Function for the Damped Oscillator | p. 216 |
| Density Operator for a Particle Coupled to a Heat Bath | p. 219 |
| Path Integral Formulation of a Damped Harmonic Oscillator | p. 223 |
| Propagator for the Damped Harmonic Oscillator | p. 224 |
| Path Integral Quantization of a Harmonic Oscillator with Complex Spring Constant | p. 230 |
| Modified Classical Action and the Propagator for the Damped Harmonic Oscillator | p. 233 |
| Path Integral Formulation of a System Coupled to a Heat Bath | p. 235 |
| Quantization of the Motion of an Infinite Chain | p. 239 |
| Quantum Mechanics of a Uniform Chain | p. 239 |
| Ground State of the Central Particle | p. 242 |
| Wave Equation for a Non-Uniform Chain | p. 244 |
| Connection with Other Phenomenological Frictional Forces | p. 246 |
| Fokker-Planck Equation for the Probability Density | p. 247 |
| The Heisenberg Equations of Motion for a Particle Coupled to a Heat Bath | p. 249 |
| Heisenberg Equations for a Damped Harmonic Oscillator | p. 249 |
| Density Matrix for the Motion of a Particle Coupled to a Field | p. 260 |
| Equations of Motion for the Central Particle | p. 263 |
| Wave Equation for the Motion of the Central Particle | p. 264 |
| Motion of the Center-of-Mass in Viscous Medium | p. 269 |
| Invariance Under Galilean Transformation | p. 272 |
| Velocity Coupling and Coordinate Coupling | p. 273 |
| Equation of Motion for a Harmonically Bound Radiating Electron | p. 274 |
| Quantum Mechanical Models of Dissipative Systems | p. 279 |
| Forced Vibration with Damping | p. 279 |
| The Wigner-Weisskopf Model | p. 282 |
| Quantum Theory of Line Width | p. 286 |
| The Optical Potential | p. 291 |
| Gisin's Nonlinear Wave Equation | p. 295 |
| Nonlinear Generalization of the Wave Equation | p. 298 |
| Dissipation Arising from the Motion of the Boundaries | p. 301 |
| Decaying States in a Many-Boson System | p. 308 |
| More on the Concept of Optical Potential | p. 315 |
| The Classical Analogue of the Nonlocal Interaction | p. 315 |
| Minimal and/or Maximal Coupling | p. 319 |
| Damped Harmonic Oscillator and Optical Potential | p. 323 |
| Quantum Mechanical Analogue of the Raleigh Oscillator | p. 326 |
| Index | p. 331 |
| Table of Contents provided by Ingram. All Rights Reserved. |
