Saved in:
Bibliographic Details
Main Author: Radozycki, Tomasz
Format: Preprint
Published: 2016
Subjects:
Online Access:https://arxiv.org/abs/1605.08202
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866913659518713856
author Radozycki, Tomasz
author_facet Radozycki, Tomasz
contents The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by incorporating into them the Heisenberg uncertainty relation between position and momentum. Even the crude form of this incorporation makes the agreement between classical and quantum distributions unexpectedly good, except for the small area, where classical momenta are large. It is demonstrated that the slight improvement of this form, makes the classical distribution very similar to the quantum one in the whole space. The obtained results are much better than those from the WKB method. The paper is devoted to ground states, but the method applies to excited states too.
format Preprint
id arxiv_https___arxiv_org_abs_1605_08202
institution arXiv
publishDate 2016
record_format arxiv
spellingShingle Classical probability density distributions with uncertainty relations for ground states of simple non-relativistic quantum-mechanical systems
Radozycki, Tomasz
Quantum Physics
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by incorporating into them the Heisenberg uncertainty relation between position and momentum. Even the crude form of this incorporation makes the agreement between classical and quantum distributions unexpectedly good, except for the small area, where classical momenta are large. It is demonstrated that the slight improvement of this form, makes the classical distribution very similar to the quantum one in the whole space. The obtained results are much better than those from the WKB method. The paper is devoted to ground states, but the method applies to excited states too.
title Classical probability density distributions with uncertainty relations for ground states of simple non-relativistic quantum-mechanical systems
topic Quantum Physics
url https://arxiv.org/abs/1605.08202