Dirac delta function
For any continuous function :
or in dimensions:
However, the limit of the normalized Gaussian function is still meaningless as a function, but some people still write such a limit as being equal to the Dirac distribution considered above in the first paragraph.
An example of how the Dirac distribution arises in a physical, classical context is available http://www.rose-hulman.edu/ rickert/Classes/ma222/Wint0102/dirac.pdfon line.
Remarks: Distributions play important roles in Dirac’s formulation of quantum mechanics.
- 1 W. Rudin, Functional Analysis, McGraw-Hill Book Company, 1973.
- 2 L. Hörmander, The Analysis of Linear Partial Differential Operators I, (Distribution theory and Fourier Analysis), 2nd ed, Springer-Verlag, 1990.
- 3 Originally from The Data Analysis Briefbook (http://rkb.home.cern.ch/rkb/titleA.htmlhttp://rkb.home.cern.ch/rkb/titleA.html)
|Title||Dirac delta function|
|Date of creation||2013-03-22 12:11:45|
|Last modified on||2013-03-22 12:11:45|
|Last modified by||PrimeFan (13766)|