Approximation properties of basis functions in variational three-body problem

Vladimir S. Vanyashin

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arXiv · physics/0009082

Approximation properties of basis functions in variational three-body problem

Vladimir S. Vanyashin

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Abstract

A new variational basis with well-behaved local approximation properties and multiple output is proposed for Coulomb systems. The trial function has proper behaviour at all Coulomb centres. Nonlinear asymptotic parameters are introduced softly: they do not destroy the self-optimized local behaviour of the wave function at vanishing interparticle distances. The diagonalization of the Hamiltonian on a finite Hilbert subspace gives a number of meaningful eigenvalues. Thus together with the ground state some excited states are also reliably approximated. For three-body systems all matrix elements are analytically obtainable up to rational functions of asymptotic parameters. The feasibility of the new basis usage has been proved by a pilot computer algebra calculation. The negative sign of an electron pair local energy at their Coulomb centre has been revealed. PACS number: 31.15.Pf

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Vladimir S. Vanyashin. 2000-09-27. Approximation properties of basis functions in variational three-body problem. https://arxiv.org/abs/physics/0009082

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