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Erschienen in:
2023 | OriginalPaper | Buchkapitel
3. Hydrogenoid Spectra with Central Perturbations
verfasst von : Matteo Gallone, Alessandro Michelangeli
Erschienen in: Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians
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Abstract
In this first chapter of ‘modern applications’ we analyse the self-adjoint realisations of hydrogenoid Hamiltonians with central, point-like perturbation and their spectral properties. On the one hand this is a classical subject, in that the self-adjoint extension problem was completed long ago by means of von Neumann’s extension scheme, but on the other hand it displays a degree of present-day topicality as a playground for the application of the Kreı̆n-Višik-Birman scheme. This point of view has been recently studied in Gallone and Michelangeli (Rep Math Phys 84:215–243, 2019), which is the reference the whole chapter is modelled on. Re-doing the analysis within this scheme, indeed, shows in which respects the latter approach is cleaner and provides more directly and naturally the characterisation of the models and their spectral content, and moreover the discussion of this Chapter allows for a useful comparison between the von Neumann and the Kreı̆n-Višik-Birman approach.