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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

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Effective action of unbounded operators on subspaces outside their domains of definition

Consider a densely defined, self-adjoint operator $$ H: \mathcal{D} \rightarrow \mathscr{H}. $$ Assume for simplicity that $H$ is nonnegative. We want to effectively restrict this operator $H$ to a s …