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The probability representation of quantum states and integral relations for Hermite and Laguerre polynomials |
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| Authors: | Anton A. Kolesnikov Vladimir I. Man’ko |
| Affiliation: | (1) Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow Region, 141700, Russia;(2) P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow, 119991, Russia |
| Abstract: | 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. |
| Keywords: | star-product symplectic tomography operator symbol Hermite polynomials probability distribution |
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