## 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.

Original language | English |
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Pages (from-to) | 2373-2384 |

Number of pages | 12 |

Journal | International Journal of Modern Physics A |

Volume | 12 |

Issue number | 13 |

DOIs | |

Publication status | Published - 20 May 1997 |

Externally published | Yes |

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