Thermodynamics of harmonic oscillator with minimal length

Abstract The generalized uncertainty principle has been applied to the Schrödinger wave equation for a one-dimensional harmonic oscillator to generate a sixth-order generalized Schrödinger equation in the position representation. The energy eigenvalues and the eigenfunctions of the sixth-order equation have been obtained. The results show the approximate correction terms of the energies due to the modified uncertainty principle. The quantum partition functions derived from the energy eigenvalue have also been used to study the thermodynamic properties of the system. The results suggest a lower bound for the minimal length equivalent to the thermal wavelength of the oscillator at very high temperature.