New relations for two-dimensional Hermite polynomials

Details New relations for two-dimensional Hermite polynomials New relations for two-dimensional Hermite polynomials

1993-12-02

arxiv.org/abs/hep-th/9312012v1

J.Math.Phys. 35 (1994) 4277-4294

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

10.1063/1.530853

The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for large values of indices are found. The applications to the squeezed one-mode states and to the time-dependent quantum harmonic oscillator are considered.

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