Eigensolutions and quantum fisher information for different potential models

Abstract

The solutions of two potentials with one potential made up of a combination of constant, Yukawa, and inversely quadratic potentials and the other made up of constant, Coulomb, and inversely quadratic potentials are obtained under the radial Schrödinger equation using the elegant parametric Nikiforov–Uvarov method. The energy equations and their corresponding wave functions are obtained in a close and compact form. The Fisher information for configuration space and momentum space are obtained for each combination of the potentials. It has been revealed that the energy eigenvalues of each combined potential model has a turning point. It is also shown that one special case in one combined potentials and another special case in the other combined potentials have equivalent energy eigenvalues. The results for the constant potential as a subset potential in each combination are not exactly the same. The Fisher information for each combined potentials and their respective subset potentials satisfied Fisher information-based uncertainty relation. It is also shown that the effect of the screening parameter on the Fisher information at the ground state and at the first excited state for one of the combining potential has a diffused format.