Analytic approximation to the energy eigenvalues of a 1D harmonic oscillator satisfying the minimal length generalized uncertainty principle

Abstract

The problem of solving for the energy eigenvalues in systems satisfying the minimal length generalized uncertainty principle has been previously treated using approximations to an infinite-order differential equation. Using the method of linear delta expansion, an analytic expression to the energy eigenvalues in a 1D harmonic oscillator satisfying the minimal length generalized uncertainty relation was derived starting with a second-order eigenvalue equation formulation. This approximation scheme was developed and applied to obtain the energy eigenvalues up to first order corrections. The result of which was found consistent with the exact result found in literature for small principal quantum number n.