Ermakov and non-Ermakov systems in quantum dissipative models
- 1 March 1986
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 27 (3) , 755-758
- https://doi.org/10.1063/1.527178
Abstract
Via the hydrodynamical formulation of quantum mechanics, a unified protocol to treat the quantum time-dependent harmonic oscillator with friction is presented, described by two different models: an explicitly time-dependent, linear Schrödinger equation (Caldirola–Kanai model) and a logarithmic nonlinear Schrödinger equation (Kostin model). For the former model, an Ermakov system that makes it possible to obtain an invariant of Ermakov–Lewis-type is derived. For the latter model, a non-Ermakov system is derived instead and it is shown that neither an exact nor an approximate invariant of Ermakov–Lewis-type exists.Keywords
This publication has 80 references indexed in Scilit:
- Gauge-independent formulation of the Aharonov-Bohm effectPhysical Review A, 1984
- Quantum treatment of Brownian motion and influence of dissipation on diffusion in dynamically disordered systemsZeitschrift für Physik B Condensed Matter, 1983
- A one dimensional microscopical model for the study of the coherence in the stopping power problem. Part 3Zeitschrift für Physik B Condensed Matter, 1983
- Microscopic derivation of a frictional Schrödinger equationPhysics Letters B, 1979
- Approaches to nuclear frictionReports on Progress in Physics, 1978
- Single-particle Schrödinger fluid. I. FormulationPhysical Review C, 1977
- Quantization of dissipative dynamical systemsPhysics Letters B, 1976
- Colliding heavy ions: Nuclei as dynamical fluidsReviews of Modern Physics, 1976
- On the theory of quantized frictionPhysics Letters B, 1975
- Relativistic Quantum Mechanics of Dyons. Exact SolutionPhysical Review D, 1971