Abstract
For his formulation of quantum mechanics P.A.M. Dirac introduced in the late 1920s so-called \(\delta \)-functions, objects that could be manipulated as functions of real variables, could be differentiated and integrated, without however being functions in a strict sense.
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References
Sobolev, S.: Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperbolyques normales Rec. Math. [Math. Sbornik] N.S. 1, 39–72 (1936)
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Dirac, P.A.M.: The principles of quantum mechanics, 4th edn. Oxford University Press, Oxford (1982) (The heuristics of the Dirac \(\delta \)-function and its derivatives are explained and extensively used in all standard physics books on quantum mechanics. None of these improve on the explanation given in Dirac’s classical book. The first edition is from 1930. The present fourth edition is still in print.)
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Treves, F.: Topological vector spaces, distributions and kernels. Academic Press, New York (1967) (A standard textbook on the topics mentioned in the title.)
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Bongaarts, P. (2015). Generalized Functions. In: Quantum Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-09561-5_25
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DOI: https://doi.org/10.1007/978-3-319-09561-5_25
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