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

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.