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

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

1995-10-04

arxiv.org/abs/hep-th/9510015v2

Int.J.Mod.Phys. A12 (1997) 2373-2384

Physics

High Energy Physics

High Energy Physics - Theory

version to appear in IJMPA, minor changes and refs. added

Scientific paper

10.1142/S0217751X97001389

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Schr\"{o}dinger 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 Schr\"{o}dinger equation for the Morse potential is obtained from the q-deformed $V=u^2+ 1/u^2$ Schr\"{o}dinger equation. Wave functions and eigenvalues of the q-Schr\"{o}dinger equations yielding a new definition of the q-Laguerre polynomials are studied.

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