An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups

Department of Mathematics, Rice University, 77005 Houston, USA

^* E-mail: zheng.gan@rice.edu

Abstract

We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schrödinger operators obtained in this context.