Function Spaces in Quantum-Mechanical Theory

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Abstract
The use of wave functions which are not normalized in the sense of quadratic integrability introduces concepts which are difficult to incorporate into the statistical interpretation of quantum-mechanical theory. A study is made of other inner-product function spaces which can be defined on the basis of the asymptotic behavior of various classes of functions. Only the cases of plane waves, cylindrical waves, and spherical waves are considered in detail. The theory offers an alternative approach to the treatment of open systems which is closer to classical field theories than is that of von Neumann.

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