English

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