Singular potentials and absorption problem in Quantum Mechanics

Abstract

We discuss a possible approach to the absorption problem in Quantum Mechanics based on using of singular attractive potentials in the corresponding Schrödinger equations. Possible criteria for selection of exact solutions of these equations are considered and it is shown that different models of absorption can be realized by a special choice of exact solutions. As an example, the motion of charged particles in the Aharonov-Bohm (AB) and the scalar attractive $ρ^{-2}$ potentials is investigated in detail. Other attractive potentials are briefly considered.