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NucEngMajor
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Homework Statement
Consider the double well potential with two wells separated by delta function in middle.
V(x) = V0 > 0 for x<-a and x>a
0 for -a<x<0 and 0<x<a
αδ for x =0
1. Find Bound state energies
2. Find odd solns and their eigenvalue equation. Give solns in graphical form
3. Repeat 2. for even
4. Plot two lowest order even and odd soln
Homework Equations
S.E
The Attempt at a Solution
I wrote down BC's noting discontinuity at delta and obtained 6 equations (think they are right?). Prof said to use the fact that the determinant of system must vanish to get energy eigenvalue equation. I don't know how to go about this. I know the other way would be incredibly long and tedious.
Aexp(-la) = Csin(-ka)+Dcos(-ka)
lAexp(-la) = Ckcos(-ka)-Dksin(-ka)
Gexp(-la) = Esin(ka) + Fcos(ka)
-lGexp(-la) = Ekcos(ka) - Fksin(ka)
D=F
k(E-C)=2mαF/h^2 (h is "h bar")[/B]