arXiv:hep-th/9510015 · International Journal of Modern Physics A

q-Schrödinger Equations for V = u2 + 1/u2 and Morse Potentials in Terms of the q-Canonical Transformation

Omer Faruk Dayi, I. H. Duru

Published May 20, 1997• 11 citations

Abstract

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Schrödinger equations for the Morse and the V = u2 + 1/u2 potentials were known to be related by a canonical transformation. q-deformed analog of this transformation connecting two different realizations of the sl q(2) algebra is presented. By the virtue of the q-canonical transformation, a q-deformed Schrödinger equation for the Morse potential is obtained from the q-deformed V = u2 + 1/u2 Schrödinger equation. Wave functions and eigenvalues of the q-Schrödinger equations yielding a new definition of the q-Laguerre polynomials are studied.

DOI: 10.1142/s0217751x97001389

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