One-parameter semigroups related to abstract quantum models of Calogero type (Q2751524)

Dunkl operators \(T_i\) \((i=1,\ldots,n)\) associated with a root system in \(\mathbb{R}^n\) are modifications of the usual partial derivatives acting on functions on \(\mathbb{R}^n\). The Hamilton operators of the Calogero model and its generalizations are related to the corresponding Laplace operators. After recalling the basic definitions, the author analyzes the spectrum of the Hamitonians, the associated heat semigroups, the Schrödinger evolution of the system and relations to generalized Hermite polynomials.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00042].