Application of Hellman-Feynman and Hypervirial theorems to the eigenvalue problem: Coulomb plus linear term and quartic anharmonic oscillator potentials

TL;DR

This paper introduces a novel method using Hellman-Feynman and Hypervirial theorems to efficiently compute high-order eigenenergy coefficients for Coulomb plus linear and quartic anharmonic oscillator potentials, bypassing eigenfunction calculations.

Contribution

It presents a fast, efficient perturbation coefficient calculation method that does not require eigenfunction coefficients, improving upon traditional Rayleigh-Schrodinger Perturbation Theory.

Findings

Method efficiently computes large order eigenenergy coefficients.

Applicable to Coulomb plus linear and quartic anharmonic oscillator potentials.

Avoids the need for eigenfunction coefficient calculations.

Abstract

We use the Hellman-Feynman (HF) and Hypervirial (HV) theorems, to calculate the perturbative coefficients of the eigenenergies formal series, in the case of the Coulomb potential with a radial linear term and the radial quartic anharmonic oscillator potential. This calculation method, contrary to the usual Rayleigh-Schrodinger Perturbation Theory (RSPT), does not require the calculation of eigenfunctions coefficients. This method is a fast and efficient tool for the calculation of large order eigenenergies coefficients.