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arXiv · 0809.1478

Value of interparticle interaction potential as a variable in solving many-body Schrödinger equation

V. M. Tapilin
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Abstract

A many-body wave function is approximated by a product of two functions: the wave function $ϕ$ depending on the particle coordinates and the function $χ$ depending only on the value of interparticle interaction potential. For the given $ϕ$ an ordinary linear differential equation for $χ$ is derived by averaging the Hamiltonian over the constant interparticle interaction potential surface. Generalized Hartree-Fock equations containing correlation effects are obtained. To test the proposed technique the ground $1^{1}S_0$ and excited $2^{3}S_1$ states of two-electron ions from H$^-$ up to Ne$^{8+}$ are calculated. In all cases the calculated energies are more accurate than those obtained with the Hartree-Fock theory even taking as $ϕ$ the symmetrized product of electron wave functions in the Coulomb field of nucleus complitly disregarded the electron-electron interaction. Variation of factors in the one-particle wave function exponents leads to the results close to those of configuration interaction approach.

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V. M. Tapilin. 2008-09-09. Value of interparticle interaction potential as a variable in solving many-body Schrödinger equation. https://arxiv.org/abs/0809.1478

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