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Advanced Physics Homework Help
Normalization of Linear Superposition of ψ States
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[QUOTE="The Head, post: 4508506, member: 321011"] [h2]Homework Statement [/h2] An electron in an infinitely deep potential well of thickness 4 angstroms is placed in a linear superposition of the first and third states. What is the frequency of oscillation of the electron probability density?[h2]Homework Equations[/h2] E=hω[h2]The Attempt at a Solution[/h2] My main problem right now is with the normalization of the wave function: I have ψTotal=Aψ1+ Bψ3 ∫|ψT|^2=1=∫(|A|^2*sin^2(pi*z/Lz) +|B|^2*sin^2(3pi*z/Lz))dz (the other terms with A*B and B*A become zero after integration) =(Lz(|A|^2+|B|^2))/2=1 So |A|^2+|B|^2=2/Lz What I'd like to do next is calculate the probability density of the electrons, but I end up with |A|^2, |B|^2, A*B, & B*A terms and don't know how to get actual numbers for all these constants, or otherwise to properly normalize this. I know what to do if the superposition of states was equally split, but it does not say that here. Any thoughts on what I'm doing wrong? Thanks [/QUOTE]
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Normalization of Linear Superposition of ψ States
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