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Arbitrary order hermite generating functions for coherent and squeezed states

Jun, 1995
8 pages
Published in:
  • Phys.Lett.A 208 (1995) 8
e-Print:
DOI:
Report number:
  • LA-UR-95-1772,
  • LA-UR-95-1772
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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 ∑n=0 ∞z jn+kHjn+k(x)/(jn+k)!\sum_{n=0}~{\infty}z~{jn+k}H_{jn+k}(x)/(jn+k)!, for arbitrary integers j≥1j\geq 1 and k≥0k\geq 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]\exp[a~j(d/dx)~j] on well-behaved functions and apply them to obtain other sums.
Note:
  • LaTeX, 8 pages