The probability representation of quantum states and integral relations for Hermite and Laguerre polynomials

被引：2

作者：

Kolesnikov, Anton A.

Man'ko, Vladimir I.

机构：

[1] State Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Region, Russia

[2] Russian Acad Sci, PN Lebedev Phys Inst, Moscow 119991, Russia

来源：

JOURNAL OF RUSSIAN LASER RESEARCH | 2007年 / 28卷 / 06期

关键词：

star-product; symplectic tomography; operator symbol; Hermite polynomials; probability distribution;

D O I：

10.1007/s10946-007-0045-0

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

Some integral relations for orthogonal polynomials are elucidated. We review the generic scheme of the star-product construction and study in detail the star-product scheme based on the tomographic map. The dual star-product operator symbols are also considered and studied. Some integral kernels related to the star-product are calculated and new integral formulas for special functions are derived.

引用

页码：594 / 609

页数：16

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