Coulomb potential V(r)=1/r problem on the Bethe lattice.

Petrova, Olga; Moessner, Roderich · Phys Rev E · 2016

basic_science · Level V

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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.