$sl_q(2)$ Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations

TL;DR

This paper develops q-deformed realizations of the SO(2,1) symmetry algebra for Kepler and oscillator potentials, introduces q-canonical transformations, and derives a q-Schrodinger equation with calculated energy spectrum and ground state.

Contribution

It presents new q-deformed realizations of the symmetry algebra and defines q-canonical transformations connecting them, along with a derived q-Schrodinger equation for Kepler-like potentials.

Findings

Derived q-Schrodinger equation for Kepler potential

Calculated energy spectrum and ground state wave function

Established q-canonical transformation framework

Abstract

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for q-canonical transformation is deduced. q-Schr\"{o}dinger equation for a Kepler like potential is obtained from the q-oscillator Schr\"{o}dinger equation. Energy spectrum and the ground state wave function are calculated.