Applications of the Jacobi group to Quantum Mechanics
Differential Geometry
2008-12-03 v1 Mathematical Physics
math.MP
Representation Theory
Optics
Abstract
Infinitesimal holomorphic realizations for the Schr\"{o}dinger-Weil representation and the discrete series representations of the Jacobi group are constructed. Explicit expressions of the basic differential operators are obtained. The squeezed states for the unitary irreducible representation of the Jacobi group are introduced. Matrix elements of the squeezed operators, expectation values of polynomial operators in infinitesimal generators of the Jacobi group, the squeezing region and a description of Mandel's parameter are presented.
Keywords
Cite
@article{arxiv.0812.0448,
title = {Applications of the Jacobi group to Quantum Mechanics},
author = {S. Berceanu and A. Gheorghe},
journal= {arXiv preprint arXiv:0812.0448},
year = {2008}
}
Comments
8 pages, Communication at the Third National Conference on Theoretical Physics, Busteni, Romania, June 10 -13, 2008, to appear in Rom. Journ. Phys. Vol 53, No 9-10, 1013-1021, 2008