Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

The Dirac Delta Function

In lecture, we introduced the Dirac delta function in order to be able to write


We defined the delta function as


(a) Use the definitions to argue the following properties of the delta function:

(b) For some applications we will have to use the delta function of a function of x rather than just of x itself. (For example when we want to integrate over momentum states -- p -- but want to conserve energy -- E = p2/2m.) Show that:


where the set of xi are the solutions (there may be more than one) of the equation

g(x) = 0.


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Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120

Last revision 13. November, 2005.