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Quantum Meachanics; Normalization in 3D

by joel.martens
Tags: normalization, quantum mechanics
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joel.martens
#1
Jun18-09, 09:11 PM
P: 16
1. The problem statement, all variables and given/known data
(1) For the cubic 3D infinite-well wave function,
[tex]\psi[/tex](x,y,z) = A sin(n[tex]\pi[/tex]x/L)sin(n[tex]\pi[/tex]y/L)sin(n[tex]\pi[/tex]z/L)
Show that the correct normalization constant is A = (2/L)[tex]^{3/2}[/tex]



2. Relevant equations
Note: The Pi's above are not meant to be superscript, and each n relates to the appropriate x,y,z
[tex]\int[/tex][tex]\psi[/tex]*[tex]\psi[/tex]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.
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Avodyne
#2
Jun18-09, 09:28 PM
Sci Advisor
P: 1,229
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
#3
Jun18-09, 09:52 PM
P: 16
Ah, thats how it comes to root A cubed. Thankyou.


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