Wigner functions in quantum mechanics with a minimum length scale arising from generalized uncertainty principle
Abstract
In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of such theories following GUP and show that the Weyl transform and the Wigner function does satisfy some of their known properties in standard quantum mechanics. We utilise the generalized Wigner function to calculate the phase space average of the Hamiltonian of a quantum harmonic oscillator satisfying deformed Heisenberg algebra. It is also shown that averages of certain quantum mechanical operators in such theories may restrict the value of the deformation parameter specifying the degree of deformation of Heisenberg algebra. All the results presented are for pure states. The results can be generalized for mixed states.
Cite
@article{arxiv.2006.11582,
title = {Wigner functions in quantum mechanics with a minimum length scale arising from generalized uncertainty principle},
author = {Prathamesh Yeole and Vipul Kumar and Kaushik Bhattacharya},
journal= {arXiv preprint arXiv:2006.11582},
year = {2021}
}
Comments
26 pages, 2 figures. The latest version contains various improvements and is an updated version containing new material. This version is accepted for publication in European Physics Journal Plus