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Dirac delta function
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(Definition)
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The Dirac delta “function”  is not a true function since it cannot be defined completely by giving the function value for all values of the argument  . Similar to the Kronecker delta, 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 people nonetheless often 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 on line.
References
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"Dirac delta function" is owned by PrimeFan. [ full author list (3) | owner history (2) ]
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Cross-references: distribution, width, limit, Gaussian, dimensions, continuous function, Kronecker delta, similar, argument, function
There are 7 references to this entry.
This is version 6 of Dirac delta function, born on 2002-01-19, modified 2008-10-17.
Object id is 1491, canonical name is DiracDeltaFunction.
Accessed 42706 times total.
Classification:
| AMS MSC: | 34L40 (Ordinary differential equations :: Ordinary differential operators :: Particular operators ) |
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Pending Errata and Addenda
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for
and
