SEMINARIO DE FISICA TEORICA I Y II

Titulo:         Heisenberg algebra, Umbral Calculus and Orthogonal Polynomials
Conferenciante: Prof. P. Winternitz (Centre de recherches mathematiques, Univ. Montreal)
Dia y hora:     27, 14:15 (Aula 8B)

Resumen:


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 M 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 of the polynomials in optics will be
discussed. The results were obtained in collaboration with G.Dattoli
and D.Levi.