dorsal/arxiv
View SchemaARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR COHERENT AND SQUEEZED STATES
| Authors | Michael Martin Nieto, D. Rodney Truax |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9506008 |
| URL | https://arxiv.org/abs/quant-ph/9506008 |
| DOI | 10.1016/0375-9601(95)00761-Q |
| Journal | Phys.Lett. A208 (1995) 8 |
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 $j\geq 1$ and $k\geq 0$. Along the way, the sums with the Hermite polynomials replaced by unity are also obtained. We also evaluate the action of the operators $\exp[a^j(d/dx)^j]$ on well-behaved functions and apply them to obtain other sums.
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"abstract": "For use in calculating higher-order coherent- and squeezed- state quantities,\nwe derive generalized generating functions for the Hermite polynomials. They\nare given by $\\sum_{n=0}^{\\infty}z^{jn+k}H_{jn+k}(x)/(jn+k)!$, for arbitrary\nintegers $j\\geq 1$ and $k\\geq 0$. Along the way, the sums with the Hermite\npolynomials replaced by unity are also obtained. We also evaluate the action of\nthe operators $\\exp[a^j(d/dx)^j]$ on well-behaved functions and apply them to\nobtain other sums.",
"arxiv_id": "quant-ph/9506008",
"authors": [
"Michael Martin Nieto",
"D. Rodney Truax"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/0375-9601(95)00761-Q",
"journal_ref": "Phys.Lett. A208 (1995) 8",
"title": "ARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR COHERENT AND SQUEEZED STATES",
"url": "https://arxiv.org/abs/quant-ph/9506008"
},
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