QM Integral and Online Integral Tables

**longbusy** · Jan17-05, 09:39 PM

Hello, I am hung up on an integral from Quantum Mechanics. I searched on Yahoo and Google for online integral tables, but failed to discover anything beyond very basic tables. The integral is as follows:

$LaTeX Code: \\int_{-\\infty}^{\\infty} \\(A*e^{-(x-a)^2} dx$

Are there any decent online integral tables that are accessible to just anyone? I found some online databases but quickly found out that I had to subscribe.

Thank You,
Jeremy

**cronxeh** · Jan17-05, 10:15 PM

Is A just a constant or a matrix?

**dextercioby** · Jan17-05, 10:30 PM

Originally Posted by cronxeh

Is A just a constant or a matrix?

The appropriate question would have bee:is A "x" dependent or not????

Daniel.

**longbusy** · Jan17-05, 10:31 PM

Oops, sorry, A is a constant. It is not dependent upon x. I could have just left that out.

**dextercioby** · Jan17-05, 10:37 PM

In that case,it can be reduced (by a simple substitution) to a Poisson integral which is doable appling the thoerem of Fubini and polar plane coordinates...

Daniel.

~~Crosson~~ · Jan17-05, 10:57 PM

What he means is, square the integral and transform to polar coordinates, then use u-substitution (inverse chain rule) to solve an easy integral, take the square root of the result.

As a side note, it is impossible to find an antiderivative for your integral. No antiderivative exits (in terms of familiar functions).

As a side-side note, if a = 0 and A = 1, the answer is sqrt(pi)