QM Integral and Online Integral Tables

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The discussion centers on the integral from Quantum Mechanics, specifically the expression \(\int_{-\infty}^{\infty} A e^{-(x-a)^2} dx\). Participants clarify that \(A\) is a constant, not dependent on \(x\), and can be simplified using a substitution to transform it into a Poisson integral. The integral lacks an antiderivative in terms of standard functions, but if \(a = 0\) and \(A = 1\), the result is \(\sqrt{\pi}\). Online integral tables were found to be limited, often requiring subscriptions for access to comprehensive resources.

PREREQUISITES
  • Understanding of Quantum Mechanics integrals
  • Familiarity with Poisson integrals
  • Knowledge of Fubini's theorem
  • Proficiency in polar coordinates transformation
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  • Research online integral tables that provide free access to advanced integrals
  • Study the application of Fubini's theorem in multiple integrals
  • Learn about the properties and applications of Poisson integrals
  • Explore techniques for transforming integrals using polar coordinates
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Students and professionals in physics, particularly those studying Quantum Mechanics, mathematicians dealing with integrals, and anyone seeking to enhance their understanding of advanced integral calculus.

longbusy
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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
 
Last edited:
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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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