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Arbitrationer
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Homework Statement
Hi everyone. This is my first time on her so I hope I make what I'm looking for clear!
The question in the book says,
If V(x) = ∞, x<0 ; -Vo, 0 < x < a ; 0, x > a
Solve the schrodinger equation for E < 0 inside and outside the well. Apply the boundary conditions at x = 0 and x = a to obtain and equation that determines the allowed values of E.
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Homework Equations
We just finished going over Finite Potential Wells. Inside the book and in class, we went over the simple case where:
V(x) = 0, -a/2 < x < a/2
V(x) = Vo, elsewhere
I think I get this. We came to the conclusion that, for one case,
ψ(x) = Ceκx for the region to the left (the, what we called in class, "classically forbidden region" (CF)), 2Acos(kx) for the center region (classically allowed (CA)) and Ce-κx for the region to the right (CF)
and for the other case:
ψ(x) = Ceκx (CF), 2iAsin(kx) (CA), -Ce-κx (CF)
Where A and C are just the constants obtained from solving the differential equation once V(x) is plugged into the Schrodinger Equation, and k is different from κ.
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The Attempt at a Solution
I wish I could say that I made an attempt. I am really confused on where to begin. Any and all help is greatly appreciated!
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