Transcription of DIRAC DELTA FUNCTION AS A DISTRIBUTION
{{id}} {{{paragraph}}}
Example: quiz answers
DIRAC DELTA FUNCTION AS A DISTRIBUTION
MASSACHUSETTS INSTITUTE OF TECHNOLOGYP hysics : Relativistic Quantum Field Theory IProf .Alan GuthMarch 13, 2008 INFORMAL NOTESDIRAC DELTA FUNCTION AS A DISTRIBUTIONWhy the DIRAC DELTA FUNCTION is not a FUNCTION :The DIRAC DELTA FUNCTION (x) is often described by considering a FUNCTION thathas a narrow peak atx= 0, with unit total area under the peak .In the limit as thepeak becomes infinitely narrow, keeping fixed the area under the peak, the functionis sometimes said to approach a DIRAC DELTA FUNCTION .One example of such a limitisg(x) lim 0g (x),( )whereg (x) 1 2 e 12x2/ 2.( )The area underg (x) is 1, for any value of >0, andg (x) approaches 0 as 0for anyxother thanx= , it was pointed out long ago that the DELTA FUNCTION cannot be rigor-ously defined this way.
If a Dirac delta function is a distribution, then the derivative of a Dirac delta function is, not surprisingly, the derivative of a distribution.We have not yet defined the derivative of a distribution, but it is defined in the obvious way.We first consider a distribution corresponding to a function, and ask what would be the
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: