Physics of the non-analytic exponential potentials

Abstract

The following work aimed to study 1-dimensional potentials which involve the absolute value of coordinate as an argument. Motivation for the following may come from several different cases. Among them is Randal-Sudrum model. I described several ways how non-analytic function might be regularized and deduce its mathematical form. The problem is discussed in the classical case of absolute-value potential and the quantum mechanical case of exponential potential.