Quantum Meachanics; Normalization in 3D

[joel.martens]

Homework Statement

(1) For the cubic 3D infinite-well wave function,
\psi(x,y,z) = A sin(n\pix/L)sin(n\piy/L)sin(n\piz/L)
Show that the correct normalization constant is A = (2/L)^{3/2}

Homework Equations

Note: The Pi's above are not meant to be superscript, and each n relates to the appropriate x,y,z
\int\psi*\psidx=1

The Attempt at a Solution

I have rearranged for A squared outside of the integral of the three sine functions (as a product) with limits of integration 0 to L. Not going to show it here becaus its long and messy. I am wondering if i need to do a triple (volume integration) or whether there is a shortcut because that's going to be one big, nasty integration :s
A little guidance would be appreciated,
Cheers, Joel.

 

[Avodyne]

Your triple integral is the product of three single integrals, each of which is the same (except for the name of the dummy integration variable).

 

[joel.martens]

Ah, that's how it comes to root A cubed. Thankyou.