In this talk we refer to the results of an article by Christian Berg and Andreas Ruffing which will be published in Commun. Math. Phys. We consider two operators and in a Hilbert space of functions on the exponential lattice
where . The operators are formal adjoints of each other and depend on a real parameter
. We show how these operators lead to an essentially unique symmetric ground state and that and are ladder operators for the sequence
. The sequence
is shown to be a family of orthogonal polynomials, which we identify as symmetrized -Laguerre polynomials. We obtain in this way a new proof of the orthogonality for these polynomials. When the polynomials are the discrete -Hermite polynomials of type II, studied in several papers on -quantum mechanics.
Seminarsko predavanje bo v sredo, 22. avgusta 2001 ob 15:15 uri
v se- minarski sobi CAMTP, Krekova 2, pritlicje.
Vljudno vabljeni vsi zainteresirani, tudi