Generalized momentum implied by GUP with a nonrelativistic harmonic oscillator

Abstract

In this paper, we consider the Schrödinger equation with a generalized form of uncertainty principle and solve the problem up to a third-order correction to the arising equation. The particle in box and harmonic oscillator cases is considered in this formulation and various thermodynamic properties are reported including entropy, internal energy, chemical potential, specific heat, etc. Various consequences of the GUP are commented.