ARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR COHERENT AND SQUEEZED STATES

Abstract

For use in calculating higher-order coherent- and squeezed- state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by ${\sum }_{n=0}^{\infty }{z}^{jn+k}{H}_{jn+k}(x)/(jn+k)!$, for arbitrary integers $j\ge 1$ and $k\ge 0$. Along the way, the sums with the Hermite polynomials replaced by unity are also obtained. We also evaluate the action of the operators $\exp [a^j(d/dx{)}^j]$ on well-behaved functions and apply them to obtain other sums.

LaTeX, 8 pages

References in corpus (1)

• Squeezed States for General Systems

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