Stability of regularizations of the Schrödinger operator with singular repulsive potential

A study is made of the stability of regularizations of a $d$-dimensional Schrödinger operator with singular repulsive potential under the assumption that the set of singularities of the potential is sufficiently thin. It is shown that for $d\geqslant2$ any positive regularization is stable and that for $d\geqslant4$ any regularization is stable. This means, in particular, that for potentials with discrete set of isolated singularities the Klauder effect can occur only in a one-dimensional quantum-mechanical system.