Hydrogenoid Spectra with Central Perturbations

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dc.contributor.areaMathematicsen_US
dc.contributor.authorGallone, Matteo
dc.contributor.authorMichelangeli, Alessandro
dc.date.accessioned2018-08-27T06:42:30Z
dc.date.available2018-08-27T06:42:30Z
dc.date.issued2018-08
dc.descriptionMathematics Subject Classification (2010) 34L10 . 34L15 . 34L16 . 47B15 . 47B25 . 47N20 . 81Q10 . 81Q80en_US
dc.description.abstractThrough the Kreĭn-Višik-Birman extension scheme, unlike the previous classical analysis based on von Neumann's theory, we reproduce the construction and classification of all self-adjoint realisations of two intimately related models: the three-dimensional hydrogenoid-like Hamiltonians with singular perturbation supported at the centre (the nucleus), and the Schördinger operators on the halfline with Coulomb potentials centred at the origin. These two problems are technically equivalent, albeit sometimes treated by their own in the the literature. Based on such scheme, we then recover the formula to determine the eigenvalues of each self-adjoint extension, which are corrections to the non-relativistic hydrogenoid energy levels.We discuss in which respect the Kreĭn-Višik-Birman scheme is somehow more natural in yielding the typical boundary condition of self-adjointness at the centre of the perturbation and in identifying the eigenvalues of each extension.en_US
dc.identifier.urihttps://openscience.sissa.it/handle/1963/35321
dc.language.isoenen_US
dc.miur.area1en_US
dc.relation.firstpage1en_US
dc.relation.ispartofseriesSISSA;34/2018/MATE
dc.relation.lastpage27en_US
dc.subjectQuantum hydrogenoid Hamiltoniansen_US
dc.subjectSchrödinger-Coulomb on halflineen_US
dc.subjectSelf-adjoint extensionsen_US
dc.subjectKreĭn-Višik-Birman theoryen_US
dc.subjectWhittaker functionsen_US
dc.subjectPoint interactionsen_US
dc.titleHydrogenoid Spectra with Central Perturbationsen_US
dc.typePreprinten_US
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