Sum rules for zeros and intersections of Bessel functions from quantum mechanical perturbation theory |
| |
Authors: | Thomas Garm Pedersen |
| |
Affiliation: | 1. Department of Physics and Nanotechnology, Aalborg University, DK-9220 Aalborg Øst, Denmark;2. Center for Nanostructured Graphene (CNG), DK-9220 Aalborg Øst, Denmark |
| |
Abstract: | 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. |
| |
Keywords: | Bessel functions Perturbation theory Quantum mechanics |
本文献已被 ScienceDirect 等数据库收录! |
|