Dirac delta function
The Dirac delta “function” , or distribution is not a true function because it is not uniquely defined for all values of the argument . Similar to the Kronecker delta symbol, the notation stands for
For any continuous function :
or in dimensions:
can also be defined as a normalized Gaussian function (normal distribution) in the limit of zero width.
Notes:
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.
References
- 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 |
---|---|
Canonical name | DiracDeltaFunction |
Date of creation | 2013-03-22 12:11:45 |
Last modified on | 2013-03-22 12:11:45 |
Owner | PrimeFan (13766) |
Last modified by | PrimeFan (13766) |
Numerical id | 16 |
Author | PrimeFan (13766) |
Entry type | Definition |
Classification | msc 34L40 |
Synonym | delta function |
Related topic | DiracSequence |
Related topic | DiracMeasure |
Related topic | Distribution4 |