Abstract
The Dirac delta function is used so extensively in quantum mechanics that we felt we should discuss it right in the beginning of the book, rather than relegating it to an appendix!
...Strictly, of course, δ(x) is not a proper function of x, but can be regarded only as a limit of a certain sequence of functions. All the same one can use δ(x) as though it were a proper function for practically all the purposes of quantum mechanics without getting incorrect results. One can also use the differential coefficients of (x), namely, δ′ (x), δ″ (x), ... , which are even more discontinuous and less ‘proper’ than δ(x) itself.
P.A.M. Dirac in The Physical Interpretation of Quantum Dynamics,
Proceedings of the Royal Society of London (A) 113, 621–641 (1926).
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References and suggested reading
P.A.M. Dirac, The Principles of Quantum Mechanics (Fourth Edition), Clarendon Press, Oxford (1958).
J. Lighthill, Introduction to Fourier Analysis and Generalised Functions, Cambridge University Press (1958).
A.K. Ghatak, I.C. Goyal and S.J. Chua, Mathematical Physics, Macmillan India Limited, New Delhi (1995).
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© 2004 Springer Science+Business Media Dordrecht
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Ghatak, A., Lokanathan, S. (2004). The Dirac Delta Function. In: Quantum Mechanics: Theory and Applications. Fundamental Theories of Physics, vol 137. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2130-5_1
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DOI: https://doi.org/10.1007/978-1-4020-2130-5_1
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