Semiclassical analysis of constrained quantum systems
Mathematical Physics
2009-11-10 v2 math.MP
Quantum Physics
Abstract
We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wave function is approximated in norm, up to terms of order hbar^(1/2), by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system.
Cite
@article{arxiv.math-ph/0312034,
title = {Semiclassical analysis of constrained quantum systems},
author = {G. F. Dell'Antonio and L. Tenuta},
journal= {arXiv preprint arXiv:math-ph/0312034},
year = {2009}
}
Comments
23 pages, a new section on submanifolds of arbitrary dimension and codimension added, references modified and added