Sum rules for zeros and intersections of Bessel functions from quantum mechanical perturbation theory

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Abstrakt

Bessel functions play an important role for quantum states in spherical and cylindrical geometries. In cases of perfect confinement, the energy of Schrödinger and massless Dirac fermions is determined by the zeros and intersections of Bessel functions, respectively. In an external electric field, standard perturbation theory therefore expresses the polarizability as a sum over these zeros or intersections. Both non-relativistic and relativistic polarizabilities can be calculated analytically, however. Hence, by equating analytical expressions to perturbation expansions, several sum rules for the zeros and intersections of Bessel functions emerge.

OriginalsprogEngelsk
TidsskriftPhysics Letters A
Vol/bind382
Udgave nummer28
Sider (fra-til)1837-1841
Antal sider5
ISSN0375-9601
DOI
StatusUdgivet - maj 2018

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