dorsal/arxiv
View SchemaApproximation properties of basis functions in variational three-body problem
| Authors | Vladimir S. Vanyashin |
|---|---|
| Categories | |
| ArXiv ID | physics/0009082 |
| URL | https://arxiv.org/abs/physics/0009082 |
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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"abstract": "A new variational basis with well-behaved local approximation properties and\nmultiple output is proposed for Coulomb systems. The trial function has proper\nbehaviour at all Coulomb centres. Nonlinear asymptotic parameters are\nintroduced softly: they do not destroy the self-optimized local behaviour of\nthe wave function at vanishing interparticle distances. The diagonalization of\nthe Hamiltonian on a finite Hilbert subspace gives a number of meaningful\neigenvalues. Thus together with the ground state some excited states are also\nreliably approximated. For three-body systems all matrix elements are\nanalytically obtainable up to rational functions of asymptotic parameters. The\nfeasibility of the new basis usage has been proved by a pilot computer algebra\ncalculation. The negative sign of an electron pair local energy at their\nCoulomb centre has been revealed.\n PACS number: 31.15.Pf",
"arxiv_id": "physics/0009082",
"authors": [
"Vladimir S. Vanyashin"
],
"categories": [
"physics.atom-ph"
],
"title": "Approximation properties of basis functions in variational three-body problem",
"url": "https://arxiv.org/abs/physics/0009082"
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