  We discuss a possible approach to the absorption problem in Quantum Mechanics
based on using of singular attractive potentials in the corresponding
Schr\"{o}dinger 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 $\rho^{-2}$ potentials is investigated in detail. Other
attractive potentials are briefly considered.
