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mtjs
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Homework Statement
I'm looking for the bound energy of a triple delta potential:
[tex]V(x) = -w \left [ \delta(x-a) + \delta(x) + \delta(x+a) \right ][/tex]
What is the correct transcendental equation for kappa?
Homework Equations
My wave function is [tex]\psi_1(x) = A e^{\kappa x}[/tex] for x < -a, [tex]\psi_2(x) = B \cosh(\kappa(x+a/2)[/tex] for -a < x < 0, [tex]\psi_3(x) = C \cosh(\kappa(x-a/2))[/tex] for 0< x < a, [tex]\psi_4(x) = D e^{-\kappa x}[/tex] forx > a.
We use this continuity formula [tex]\psi'( z+\epsilon) - \psi'(z-\epsilon) = -\frac{2mw}{\hbar^2} \psi(z)[/tex]
The Attempt at a Solution
Calculating the continuity formula at x = 0 gives [tex]\kappa \tanh(\frac{\kappa a}{2}) = \frac{m w}{\hbar^2}[/tex]
This means, you get the same bound energy as for one delta potential if a is very large, and something weird for small a?
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