q-Schrodinger Equations for V=u^2+ 1/u^2 and Morse Potentials in terms of the q-canonical Transformation

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 $V=u^2+1/u^2$ 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 $V=u^2+1/u^2$ Schrödinger equation. Wave functions and eigenvalues of the q-Schrödinger equations yielding a new definition of the q-Laguerre polynomials are studied.

arXiv commentversion to appear in IJMPA, minor changes and refs. added

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