Shape Invariance in Deformation Quantization

Constantin Rasinariu

Abstract Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the implications of the supersymmetric quantum mechanics and shape invariance techniques to the phase space formalism. We show that shape invariance induces a new set of relations between the Wigner functions of the system, that allows for their direct calculation, once we know one of them. The simple harmonic oscillator and the Morse potential are solved as examples.

Jaromir Tosiek

A N F Aleixo, A. B. Balantekin, M A Cândido Ribeiro

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q -deformed ladder operators. We show that these new ladder operators satisfy new q -deformed commutation relations. In this context we construct an alternative q -deformed model that preserves the shape-invariance property presented by the primary system. q -deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

F. Bayen, Mosh� Flato, Christian Frønsdal +2 more

Gu Zhi-Yu

This article shows that for all one dimensional shape invariant potentials with parameters related by translation we can find their multiparameter deformations with q acting as the deformation parameter.

Maciej Przanowski, Francisco J. Turrubiates