ASYMPTOTICS OF THE EIGENVALUES OF THE SCHRÖDINGER OPERATOR

We examine the selfadjoint operator in . We assume that the potential tends to as . Under these conditions the spectrum of is discrete. In the paper the well-known asymptotic formula (*)for the distribution function of the eigenvalues is justified under very weak assumptions on , namely the following conditions: 1) , where . 2) almost everywhere when . 3) There exist a continuous function , , , and an index such that for any , , .Bibliography: 12 items.