A q-Deformation of the Harmonic Oscillator

TL;DR

This paper explores a q-deformed harmonic oscillator using q-deformed phase space, revealing unique spectral features, eigenfunctions with lattice structure, and novel degeneracies not seen in the classical case.

Contribution

It introduces a formulation of the q-deformed harmonic oscillator in terms of canonical variables and uncovers unexpected spectral and eigenfunction properties.

Findings

Spectral degeneracy and additional energy levels.

Eigenfunctions exhibit lattice structure.

Unanticipated features in the spectrum and eigenstates.

Abstract

The q-deformed harmonic oscillator is studied in the light of q-deformed phase space variables. This allows a formulation of the corresponding Hamiltonian in terms of the ordinary canonical variables $x$ and $p$. The spectrum shows unexpected features such as degeneracy and an additional part that cannot be reached from the ground state by creation operators. The eigenfunctions show lattice structure, as expected.