The basics of (linear) unbounded self-adjoint operators is discussed in this chapter. Cayley transform, von Neumann criterion on self-adjoint extensions, Weyl spectral criterion and many examples are presented. These are the first steps to the mathematical formulation of quantum mechanics. From now on the Hilbert spaces are supposed to be separable and, unless it is explicitly remarked, also complex.
KeywordsUnitary Operator Energy Operator Adjoint Operator Hermitian Operator Linear Isometry
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