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Quantum Meachanics; Normalization in 3D 
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#1
Jun1809, 09:11 PM

P: 16

1. The problem statement, all variables and given/known data
(1) For the cubic 3D infinitewell 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. 


#2
Jun1809, 09:28 PM

Sci Advisor
P: 1,204

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).



#3
Jun1809, 09:52 PM

P: 16

Ah, thats how it comes to root A cubed. Thankyou.



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