Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations

Preprint
Publisher Website
Google Scholar
  • 21 November 2001
Abstract
We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the position and momentum are assumed to obey the minimal length uncertainty relations. These relations exhibit a specific realization of the UV/IR correspondence which appears in string theory. Our solutions illustrate the way such minimal length uncertainties affect simple quantum mechanical systems in arbitrary dimensions, and suggest their effects could be detected in precision experiments involving electrons trapped in magnetic fields. The result may also provide a new perspective on the computation of the cosmological constant.

This publication has 0 references indexed in Scilit: