Q analogs of the radial Schrödinger equation in N space dimensions.

Abstract

Transparent closed forms of the radial ${\mathrm{SO}}_{\mathit{q}}$(N) Schr\"odinger equation acting on the noncommutative quantum Euclidean space are written both for l=0 and l\ensuremath{\ne}0. Starting from the s-wave equation leads to the derivation of an alternative q analog of the radial Schr\"odinger equation in N space dimensions exhibiting a modified symmetry, now in terms of wave functions depending on the radial coordinate only. The harmonic oscillator and the Coulomb system are treated as concrete examples. These results open the way to the derivation of q-deformed (1/N)-energy formulas for arbitrary spherically symmetrical potentials. Comparisons with exact ${\mathrm{SO}}_{\mathit{q}}$(N) results, as well as further interpretations, have also been made.