A $q$-deformation of the Coulomb Problem

TL;DR

This paper extends the algebra of observables in $SO_q(3)$-symmetric quantum mechanics to include the inverse radial coordinate, enabling the derivation of eigenvalues and eigenfunctions for a $q$-deformed Coulomb Hamiltonian.

Contribution

It introduces a $q$-deformation of the Coulomb problem by extending the algebra of observables to include the inverse radial coordinate, facilitating spectral analysis.

Findings

Derived eigenvalues of the $q$-deformed Coulomb Hamiltonian.

Obtained eigenfunctions within the $q$-deformed framework.

Extended the algebra of observables to include inverse radial coordinate.

Abstract

The algebra of observables of $SO_{q}(3)$-symmetric quantum mechanics is extended to include the inverse $\frac{1}{R}$ of the radial coordinate and used to obtain eigenvalues and eigenfunctions of a \q-deformed Coulomb Hamiltonian.