Analytical Solutions to The Schrödinger Equation with Collective Potential Models: Application to Quantum Information Theory

Abstract

In this study, the energy equation and normalized wave function were obtained by solving the Schrödinger equation analytically utilizing the Eckart-Hellmann potential and the Nikiforov-Uvarov method. Fisher information and Shannon entropy were investigated. Our results showed higher-order characteristic behavior for position and momentum space. Our numerical results showed an increase in the accuracy of the location of the predicted particles occurring in the position space. Also, our results show that the sum of the position and momentum entropies satisfies the lower-bound Berkner, Bialynicki-Birula, and Mycieslki inequality and Fisher information was also satisfied for the different eigenstates. This study's findings have applications in quantum chemistry, atomic and molecular physics, and quantum physics.