q – Schrödinger Equations for V = u 2 + 1 / u 2 and Morse Potentials in terms of the q – canonical Transformation
نویسنده
چکیده
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. E-mail address: [email protected]. E-mail address: [email protected].
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