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$$\pi$$x/L)sin(n$$\pi$$y/L)sin(n$$\pi$$z/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
$$\int$$$$\psi$$*$$\psi$$dx=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.