Analytical solution of the Schrödinger equation for isotropic velocity-dependent potentials

Abstract

The energy spectrum of the velocity-dependent potentials with respect to the harmonic oscillator potential and Coulomb potential are obtained for any and quantum states using the Nikiforov–Uvarov method for different cases of velocity-dependent terms. The effects of isotropic velocity-dependent potentials on the bound state energy eigenvalues are examined in analytic form when the form factor is considered as and As an application to a physical system, we evaluated the vibrational partition function and other thermodynamic properties for the isotropic velocity-dependent potential harmonic oscillator.