Abstract
Publisher Summary This chapter discusses the quantum kinematics of unbounded observables. In general, the self-adjoint operators (even if they are bounded) have not only discrete but also a continuous set of eigenvalues. However, only the eigenvectors of the discrete set of eigenvalues belong to a Hilbert space. The scalar product is not defined for eigenvectors, which cannot be normalized. A natural way out of this difficulty is the introduction of a rigged Hilbert space.
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