Essential Self-Adjointness of Generalized Schroedinger Operators

摘要

We give a necessary and sufficient condition for the generalized Schroedinger operator to be essentially self-adjoint in L exp 2 ( omega ; rhodx), under general assumptions on rho and for arbitrary domains omega in Rsup(n). In particular, if rho is strictly positive and locally Lipschitz continuous on omega = Rsup(n), then A is essentially self-adjoint. We also give examples of non-essential self-adjointness and a complete discussion of the one-dimensional case. These results have applications to the problem of the essential self-adjointness of quantum Hamiltonians and to the uniqueness problem of Markov processes. (Atomindex citation 15:054086)