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A multipoint perturbation formula for eigenvalue problems (2305.08151v1)
Published 14 May 2023 in math-ph, cs.NA, math.MP, math.NA, math.SP, and quant-ph
Abstract: Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of a Hamiltonian where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several nearby Hamiltonians are known, standard perturbation theory cannot simultaneously use all this knowledge to provide a better approximation. We derive a formula enabling such an approximation result, and provide numerical examples for which this method is more competitive than standard perturbation theory.
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