Simos, TEMaroulis, GXiong, Z.Μπακάλης, Ναούμ Χ.Karaoulanis, D.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.MELVILLE372-375ISBN: 978-0-7354-0685-80094-243Xhttps://hdl.handle.net/10442/12643engSpringer New York LLC© AMER INST PHYSICS© AMER INST PHYSICSInternational 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 - 2008-09-30Physics, MultidisciplinaryExcited statesVariational minimizationPhysics, AppliedRemarks on the Hylleraas-Undheim and MacDonald Higher Roots, And Functionals Having Local Minimum at The Excited StatesΑνακοίνωση σε συνέδριο2009ΦυσικήPhysical sciencesFrascati 42Άρθρο συνεδρίουConference articleΕθνικό Ίδρυμα Ερευνών (ΕΙΕ)Greek Aggregator OpenArchives.gr | National Documentation Centre (EKT)