Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 29.4.2008 |
| Speaker: | Pavel Winternitz, CRM, Université de Montréal |
| Title: | Heisenberg algebra, Umbral Calculus and Orthogonal Polynomials |
| Abstract: | (spoluautoři: G. Dattoli and D. Levi) Umbral calculus can be viewed as an abstract theory of the Heisenberg commutation relation $[P,M]=1$. In ordinary quantum mechanics $P$ is the derivative and $x$ the coordinate operator. Here we shall realize $P$ as a second order differential operator and $M$ as a first order integral one. We show that this makes it possible to solve large classes of differential and integro-differential equations and to introduce new classes of orthogonal polynomials, related to Laguerre polynomials. Applications in optics and astrophysics will be mentioned. |
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