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 n and l 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 ( )2 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.

Thermodynamic properties of improved deformed exponential-type potential (IDEP) for some diatomic molecules

“…The vibrational and rotational energy levels of different potential energy models [11][12][13][14] have been established to play a key role in determining partition function of any system [15].…”

Energy eigenvalue spectra and applications of the sextic and the Coulomb perturbed potentials

“…The NUFA method is regarded as a combination of Nikiforov Uvarov (NU) [54], the parametric NU [55] and the functional analysis methods. This method is basically used to solve a second-order differential equation of the form [56,57]…”

Solutions of the Schrödinger equation with velocity-dependent potentials:a study on Kratzer, Mie and Hulthen potentials

“…However, no study has taken into account the effect of velocity-dependent potentials. This paper focuses on resolving the solution for the velocity-dependent versions of the Kratzer, Mie, and Hulthen potentials, considering a constant value for the form factor r 0 ( ) e gr = [40]. The present work is organized as follows: section 2 provides a concise introduction to the NU method.…”