Coulomb potentialproblem on the Bethe lattice
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- 11 January 2016
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 93 (1) , 012115
Abstract
We study the problem of a particle hopping on the Bethe lattice in the presence of a Coulomb potential. We obtain an exact solution to the particle's Green's function along with the full energy spectrum. In addition, we present a mapping of a generalized radial potential problem defined on the Bethe lattice to an infinite number of one-dimensional problems that are easily accessible numerically. The latter method is particularly useful when the problem admits no analytical solution.Keywords
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Funding Information
- Alexander von Humboldt-Stiftung
- Deutsche Forschungsgemeinschaft (SFB 1143)
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