1304.3281 (Fumio Hiroshima et al.)

On periodic wave functions of Schrödinger operators on Cayley trees    [PDF]

Fumio Hiroshima, Utkir Rozikov

In the paper we define periodic wave functions for a (discrete) Schr\"odinger operator on a Cayley tree. This periodicity depends on a subgroup of a group representation of the Cayley tree. For any subgroup of finite index we give a criterion for eigenvalues of the Schr\"odinger operator under which there are periodic wave functions. For a normal subgroup of infinite index we describe a class of periodic wave functions.

View original: http://arxiv.org/abs/1304.3281