Path integral for the harmonic oscillator in one dimension with nonzero minimum position uncertainty

We use the path integral formalism in momentum space representation to determine the energy eigenvalues and eigenfunctions of the harmonic oscillator in one dimension with nonzero minimum position uncertainty given by (Δx)min=ℏβ where β   is the deformation parameter of the modified commutation relation [x,p]=iℏ(1+βp2)[x,p]=iℏ(1+βp2). We check the correctness of our results by rederiving the energy eigenvalues and eigenfunctions of the usual harmonic oscillator.