Applications of the Jacobi group to Quantum Mechanics

Details Applications of the Jacobi group to Quantum Mechanics Applications of the Jacobi group to Quantum Mechanics

2008-12-02

arxiv.org/abs/0812.0448v1

Mathematics

Differential Geometry

8 pages, Communication at the Third National Conference on Theoretical Physics, Busteni, Romania, June 10 -13, 2008, to appear

Scientific paper

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.

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