A multipoint perturbation formula for eigenvalue problems

• URL: http://arxiv.org/abs/2305.08151v1
• Date: Sun, 14 May 2023 13:06:09 GMT
• Title: A multipoint perturbation formula for eigenvalue problems
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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