Véronique Hussin (Université de Montréal, DMS et CRM)

Title: Correspondence between ladder functions and operators for classical and quantum exactly solvable systems

Abstract: In recent years, ladder functions have been defined in the context of the Hamiltonian formalism of classical mechanics, and a strong correspondence has been observed for many systems between the classical and quantum objects in terms of their functional dependence on the canonical variables x and p. Indeed, ladder functions were constructed for a class of simple solvable classical systems and their form computed by analogy with the form of the corresponding well-known quantum ladder operators. This raised the question as to whether the analogy could be further pursued for more elaborated systems. In particular, the ladder functions of the one-dimensional classical and quantum systems known as Rosen-Morse were missing in preceding approaches. We discovered that the classical ladder functions are considerably more elaborate. We will thus discuss the procedure to get them as some product of factor functions. We also extend this procedure to the quantum case in order to find the corresponding ladder operators.