**Required math: calculus **

**Required physics: none**

Reference: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 2.23.

Here are a few simple examples of integrals involving the Dirac delta function. The delta function is defined by the two conditions:

Since it is zero everywhere except at it follows that

for any ‘ordinary’ function . A simple extension of this is

This follows by making the substitution . Then and we get

This integral is provided the limits of integration include , that is, , or .

For example

Another example:

And a final example:

since the limits of integration don’t include .

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Dells94nice explanation. thank u guys

DamiHi, Please could you explain the last example better? I don’t understand the statement “since the limits of integration don’t include {x=2}. ” and how it applies to the solution. Thanks

gwrowePost authorSince is zero everywhere except at , the integral for any function , since the range of integration (from to ) doesn’t contain the point .

manojr=2 I.e

This value may be lies between lower limit and upper limerotherwise it should be zero

If it lies between limit ex limit is -4 to 4

Then we put r=2in f2f and get answer