\(Q\)-deformed inverse scattering problem. (English) Zbl 0835.35126

Hruby, J.

Bureš, J. (ed.) et al., Proceedings of the winter school on geometry and physics, Zdíkov, Czech Republic, January 1993. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 37, 103-114 (1994).

Summary: Starting from the physical point of view on the Miura transformation as reflectionless potential and its connection with supersymmetry we define a scaling \(q\)-deformation of this to obtain \(q\)-deformed supersymmetric quantum mechanics. An application to an inverse scattering problem is given.
For the entire collection see [Zbl 0823.00015].

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35P25	Scattering theory for PDEs
81U40	Inverse scattering problems in quantum theory
81Q60	Supersymmetry and quantum mechanics
82B23	Exactly solvable models; Bethe ansatz

Keywords:

Miura transformation; reflectionless potential; supersymmetry; \(q\)- deformation