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

S. Rekab·N. Zenine
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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.

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S. Rekab, N. Zenine. 2006-02-12. Application of Hellman-Feynman and Hypervirial theorems to the eigenvalue problem: Coulomb plus linear term and quartic anharmonic oscillator potentials. https://arxiv.org/abs/math-ph/0602029

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