Properties of a smooth, dense, invariant domain for singular potential Schroedinger operators

• URL: http://arxiv.org/abs/2305.06718v1
• Date: Thu, 11 May 2023 10:54:14 GMT
• Title: Properties of a smooth, dense, invariant domain for singular potential Schroedinger operators
• Authors: Thomas Thiemann
• Abstract summary: We show that relevant matrix elements and inner products can be computed analytically in closed form. This provides the required data for an analytical Gram-Schmid orthonormalisation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it would be desirable to have at one's disposal an explicit basis spanning a dense and invariant domain for such types of Schr\"odinger operators, for instance stationary perturbation theory or the Raleigh-Ritz method. Here we make the observation, that not only a such basis can indeed be provided but that in addition relevant matrix elements and inner products can be computed analytically in closed form, thus providing the required data e.g. for an analytical Gram-Schmid orthonormalisation.

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