Integral Tables for Quantum Mechanics

[budullewraagh]

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

[NeonBlack]

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]

[swansont]

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/

[BenTheMan]

budullewraagh---

 

you need a position or momentum space representation for psi. Then you can do the integrals at integrals.com.

 

Actually, if you are a physics udergrad, you should own a copy of this book. Seriously.

 

If you go to grad school, you may eventually need this book.

[budullewraagh]

Yeah, I apologize; the latex didn't work out for me. Actually, the integral I was looking for was available at sosmath.com; I was computing an expectation value for the radius of the He+ cation for my physical chemistry course. Thanks anyway for your help!

[ajb]

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?

[Norman Albers]

Here's a little more LaTex: [math] \int_0^\infty dr \Psi^*\Psi [/math] or maybe if angular integrations are not yet done, [math] \int d^3V \Psi^* \Psi [/math]. You don't want to hear my attitude toward normalization! I have spoken here: http://www.scienceforums.net/forum/showthread.php?t=24832&highlight=normal+modes .