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Remarks on the Hylleraas-Undheim and MacDonald Higher Roots, And Functionals Having Local Minimum at The Excited States

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Remarks on the Hylleraas-Undheim and MacDonald Higher Roots, And Functionals Having Local Minimum at The Excited States
Xiong, Z.
Μπακάλης, Ναούμ Χ.
Karaoulanis, D.
Simos, TE (EN)
Maroulis, G (EN)
Ανακοίνωση σε συνέδριο
2009
The excited states, being energy saddle points in the Hamiltonian eigenfunction Hilbert space, cannot be computed variationally by minimization of the energy. Thus, functionals are presented, that have local minimum at the bound excited states of a non-degenerate Hamiltonian, allowing the computation at any desired accuracy, by using crude approximations of the lower lying states. They are useful for larger systems, because the higher roots of the standard secular equation have, by the Hylleraas-Undheim and MacDonald theorem, several restrictions, which render them of lower quality relative to the lowest root, if the latter is good enough. Preliminary test-results are presented for He (1)S 1 s2s.
MELVILLE
Φυσική (EL)
Physics (EN)
Physics, Multidisciplinary
Excited states
Variational minimization
Physics, Applied
English
Springer New York LLC
International Conference on Computational Methods in Science and Engineering, Hersonissos, GREECE, Computational Methods in Science and Engineering, Vol 2: Advances in Computational Science, 2008-09-25 - 2008-09-30
© AMER INST PHYSICS
© AMER INST PHYSICS (EN)
National Hellenic Research Foundation (NHRF)
Helios - Repository of the National Hellenic Research Foundation (NHRF)



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