Schrödinger operators with singular potentials and magnetic fieldsстатья
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Дата последнего поиска статьи во внешних источниках: 27 октября 2021 г.
Аннотация:A formal Schrödinger operator of the form H = (-i∂/∂x + A(x))2 + V(x) in ℝd is considered, where A is a bounded measurable vector-valued function and both V(x) and div A are measures satisfying certain additional conditions. It is shown that one can give meaning to such an operator as a lower bounded self-adjoint operator in L 2(ℝd). The corresponding heat kernel is constructed and its small-time asymptotics are obtained. A rigorous Feynman path integral representation for the solutions of the heat and Schrödinger’s equations with generator H is given.