Effect of electric and magnetic field on thermal property of two dimensional harmonic oscillator

The energy spectrum of a 2D quantum harmonic oscillator confined by a hard wall circular cavity of size r(0) in the presence of static electric and the magnetic field is computed numerically using the Bessel function basis set and the linear variational process. The effect of the size of the circular cavity, magnetic field, and electric field strength is studied on the energy levels, the radial transition matrix elements, and the thermal properties of the system like specific heat, Helmholtz free energy, and entropy using canonical partition function. Blueshift is observed for an increase in magnetic and electric field strength. The harmonic oscillator problem is critical for understanding any natural system that undergoes deformation and performs simple harmonic motion.