Coordinate formalism on abstract Hilbert space: Kinematics of a quantum measurement.
Coordinate form of tensor analysis on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear isometries. Quantum measurement and collapse are interpreted as isometric functional transformations. Several experiments including the two-slit experiment are analyzed in the new context.
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