Quantum Smooth Boundary Forces from Constrained Geometries
Abstract
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is illustrated with the basic example of the one-dimensional motion of a free particle in an interval, and yields a fuzzy boundary, a position-dependent mass (PDM), and an extra potential on the quantum level. The consistency of our quantization is discussed by analyzing the semi-classical phase space portrait of the derived quantum dynamics, which is obtained as a regularization of its original classical counterpart.
Cite
@article{arxiv.1902.07305,
title = {Quantum Smooth Boundary Forces from Constrained Geometries},
author = {J. -P. Gazeau and T. Koide and D. Noguera},
journal= {arXiv preprint arXiv:1902.07305},
year = {2019}
}
Comments
22 pages, 14 figures, the title was changed, many references for the position-dependent mass were delited, the published version in J. Phys. A