THE q-DEFORMED SCHRÖDINGER EQUATION OF THE HARMONIC OSCILLATOR ON THE QUANTUM EUCLIDEAN SPACE
Ursula Carow-Watamura, Satoshi Watamura
We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.
arXiv:hep-th/9309160•International Journal of Modern Physics A•Sep 10, 1994•17 citations