Modern Physics Letters A

THE q-SCHRÖDINGER EQUATION

Joseph A. Minahan

Published Dec 20, 1990• 148 citations

Abstract

We consider the Schrödinger equation for the one-dimensional harmonic oscillator, but with the normal derivative replaced by a q-derivative. The normalizable solutions are found and the q-generalization of the Hermite polynomials is given. The free equation is also considered, but no normalizable eigenstates exist even if the system is in a box.

DOI: 10.1142/s021773239000305x

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