The First Order Effect of the Quantum Weyl Algebra on a Harmonic Oscillator

TL;DR

This paper explores how a first-order expansion of the quantum Weyl algebra influences a quantum harmonic oscillator, revealing emergent magnetic and dissipative effects in a slightly noncommutative space.

Contribution

It introduces a first-order realization of the quantum Weyl algebra applied to a harmonic oscillator, uncovering novel magnetic and dissipative phenomena.

Findings

A magnetic field appears in the perturbed system.

A dissipative term emerges in the Hamiltonian.

Noncommutative space affects quantum harmonic oscillator behavior.

Abstract

We examine a concrete realization of the quantum Weyl algebra and expand it to first order. From here we apply the resulting algebra to a quantum harmonic oscillator in its ground state and observe how a slightly noncommutative space affects the physical system. The main result is, similar to a free particle a magnetic field appears, but a new observation is that a dissipative term appears in the perturbed Hamiltonian as well.