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Integral Tables for Quantum Mechanics


budullewraagh
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Does anyone know where I can find integral tables for QM? I tried a few, but they cannot be solved as indefinite integrals that give rise to noninfinite quantities. Example:

 

[math]

r=\int_{0}^{\infty} (&\X\Psi*(x))(&\X\Psi(x))*4*&\X\pi*r^2*dr

[/math]

<r>=(integral, 0 to infinity) (psi(x))*(psi*(x))dr

 

Using integration by parts gives a solution that goes to infinity. Can anyone help me find some tables?

 

Thanks,

 

Clark

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Most of the integrals in basic QM shouldn't require a table. What exactly is the psi function you are working with? I see 1 problem and 1 potential problem.

Problem: If you want the average r, you need [math]\int r \Psi^2dr[/math]

Potential Problem: I notice you aren't diving by [math]\int \Psi^2dr[/math]

If psi is normalizable and already normalized, then you don't need to do this.

 

So in general, this is what you want:

 

[math]<r>=\frac{\int r \Psi^2 dr}{\int \Psi^2 dr}[/math]

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CRC handbook has integral tables. I like Dwight, Table of Integrals and Other Mathematical Data, though my edition didn't have a gaussian integral in it (!). Of course, you can compile your own list as you find solutions, and find them on the intertubes.

 

http://en.wikipedia.org/wiki/Table_of_integrals

http://integral-table.com/IntegralTable.pdf (<—— pdf)

http://www.math.unb.ca/sections/integrals/

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  • 2 weeks later...

Something similar I have wanted is a list of the classes of potentials that the Schrödinger equation is exactly solvable in the sense that the wave function can be written in terms of elementary and special functions.

 

I imagine that the list is not huge.

 

Anybody seen such a list?

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