# Quantum Meachanics; Normalization in 3D

by joel.martens
Tags: normalization, quantum mechanics
 P: 16 1. The problem statement, all variables and given/known data (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)$$^{3/2}$$ 2. Relevant 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 3. 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 thats going to be one big, nasty integration :s A little guidance would be appreciated, Cheers, Joel.