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On the Raleigh-Ritz variational method. Non-orthogonal basis set

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arxiv 2405.10340 v1 pith:OGJXNDL2 submitted 2024-05-14 quant-ph

Francisco M. Fernández This is my paper · ORCID
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keywords methodvariationalbasisconnectiondiagonalizationdiscussequationshermitian
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We overview the main equations of the Rayleigh-Ritz variational method and discuss their connection with the problem of simultaneous diagonalization of two Hermitian matrices.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the application of the Rayleigh-Ritz method to a projected Hamiltonian

    quant-ph 2024-11 accept novelty 6.0 of 10

    For a particle-in-a-box toy model, Rayleigh-Ritz eigenvalues for a projected Hamiltonian converge from below (mostly), unlike the usual upper-bound behavior, with exact zero eigenvalues for the null space.

  2. On the exact solutions of a two-dimensional hydrogen atom in a constant magnetic field

    quant-ph 2025-06 conditional novelty 4.0 of 10

    The polynomial quasi-exact solutions for the 2D hydrogen atom in a magnetic field match true eigenstates only at special field strengths, so they are not the full spectrum.

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