Deficiency Indices and Singular Boundary Conditions in Quantum Mechanics

摘要

We consider Schroedinger operators H in L exp 2 (Rsup(n)), n from IN, with countably infinitely many local singularities of the potential which are separated from each other by a positive distance. It is proved that due to locality each singularity yields a separate contribution to the deficiency index of H. In the special case where the singularities are pointlike and the potential exhibits certain symmetries near these points we give an explicit construction of self-adjoint boundary conditions. (ERA citation 11:012401)