q-Schrodinger Equations for V=u²+ 1/u² and Morse Potentials in terms of the q-canonical Transformation
Dayi, O. F. · Duru, I. H.
Original · EN
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 slq(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.
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