A Hamiltonian yielding damped motion in an homogeneous magnetic field: quantum treatment

DOI

10.1080/14029251.2019.1591719How to use a DOI?

Keywords

dissipative systems; quantization; Hamiltonian mechanics

Abstract

In earlier work, a Hamiltonian describing the classical motion of a particle moving in two dimensions under the combined influence of a perpendicular magnetic field and of a damping force proportional to the particle velocity, was indicated. Here we derive the quantum propagator for the Hamiltonian in different representations, one corresponding to momentum space, the other to position, and the third to a natural choice of “velocity” variables. We call attention to the following noteworthy fact: the Hamiltonian contains three parameters which do not in any way influence the motion of the position of the particle. However, at the quantum level, the propagator, even in the position representation, depends in an intricate way on these classically irrelevant parameters. This creates considerable doubt as to the validity of such a quantization procedure, as the physical results predicted differ for various Hamiltonians, all of which describe the dissipative dynamics equally well.

Copyright

© 2019 The Authors. Published by Atlantis and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - François Leyvraz
AU  - Francesco Calogero
PY  - 2021
DA  - 2021/01/06
TI  - A Hamiltonian yielding damped motion in an homogeneous magnetic field: quantum treatment
JO  - Journal of Nonlinear Mathematical Physics
SP  - 228
EP  - 239
VL  - 26
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1591719
DO  - 10.1080/14029251.2019.1591719
ID  - Leyvraz2021
ER  -