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DIRAC DELTA FUNCTION - Physicspages

DIRAC DELTA FUNCTIONLink to: Physicspages home leave a comment or report an error, please use the auxiliary date: Original: 16 Feb 2011, 14 Nov 2011, 6 Feb 2017; Revised 26 Dec DIRACDELTAFUNCTION IN ONE DIMENSIONOne of the weirder bits of mathematics that the physics student will en-counter is the DIRAC DELTA FUNCTION (x). In one dimension, the FUNCTION (technically it s really not a FUNCTION at all, but a distribution) can be definedby saying (x) =0 for allx6=0 but (x) = atx=0. However, this def-inition isn t very satisfactory, and in fact doesn t define (x)uniquely.

delta function that I mentioned at the start. There are many way we can define a function that is zero everywhere but infinite at x= 0. Look at it this way. Instead of using the limit of the sequence of rectangles that I did at the start, suppose we use a sequence of rectangles of width 1=kwand height w, so that their areas are all 1=k.

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