A Hamiltonian yielding damped motion in an homogeneous magnetic field: quantum treatment. Issue 2 (3rd April 2019)

• Record Type: Journal Article
• Authors: Leyvraz, François; Calogero, Francesco
• Is Part Of: Journal of nonlinear mathematical physics. Volume 26:Issue 2(2019)
• Page Start: 228
• Page End: 239
• Publication Date: 2019-04-03
• Subjects: dissipative systems -- quantization -- Hamiltonian mechanics; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2019.1591719
• Languages: English
• ISSNs: 1402-9251

Abstract

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.