QM Integral and Online Integral Tables

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The discussion focuses on a specific integral from Quantum Mechanics, \int_{-\infty}^{\infty} \(A*e^{-(x-a)^2} dx, and the difficulty in finding comprehensive online integral tables. Users express frustration over the lack of accessible resources, often encountering subscription-based databases. It is clarified that A is a constant, not dependent on x, allowing for simplification using a Poisson integral approach. The integral cannot be expressed in terms of familiar functions, but if a = 0 and A = 1, the result simplifies to sqrt(pi). Overall, the conversation highlights the challenges of finding useful integral resources and solving complex integrals in Quantum Mechanics.
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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:

\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
 
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Is A just a constant or a matrix?
 
cronxeh said:
Is A just a constant or a matrix?

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


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

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