Pseudo perturbative expansion method; the non-polynomial, cutoff - Coulomb, and Coulomb plus logarithmic potentials

TL;DR

This paper introduces a new analytical expansion method for solving Schrödinger equations with complex potentials, demonstrating its effectiveness on various non-polynomial and Coulomb-related potentials, and critically examines the accuracy of existing large N expansion methods.

Contribution

It presents a novel pseudo perturbative expansion technique applicable to non-polynomial and Coulomb potentials, improving analytical solutions for complex quantum systems.

Findings

Successfully applied to rational non-polynomial oscillator potential

Analyzed the accuracy of large N expansion methods, challenging previous conclusions

Extended the method to cutoff-Coulomb and Coulomb plus logarithmic potentials

Abstract

We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a conclusion reached by Scherrer et al. [2], via matrix continued fractions method, that the shifted large N expansion method leads to dubious accuracies is investigated. The cutoff - Coulomb and Coulomb plus logarithmic potentials are also investigated.