Algebraic method for the harmonic oscillator with a minimal length

TL;DR

This paper extends the algebraic solution method of the harmonic oscillator to a non-commutative framework, addressing modifications due to minimal length considerations.

Contribution

It introduces an algebraic approach for solving the harmonic oscillator in a non-commutative setting with minimal length.

Findings

Algebraic method adapted to non-commutative case

Solution for harmonic oscillator with minimal length

Potential implications for quantum mechanics

Abstract

We show that the algebraic method solving the ordinary harmonic oscillator can be adapted to the non-commutative case.