# Bound States in a Double Delta Function Potential [closed]

Let $V(x) = −u \delta(x) - v \delta(x − a)$ where $u, v > 0$ correspond to a potential with two $\delta$ wells. Let $v > u$. If $a$ is very large, there is certainly a bound state: the particle sits in the $\delta$-well. As $a$ decreases to a certain critical value, the bound state disappears. I need help finding that value.

My idea was: Before the bound state disappears, its energy approaches $0$. I'm trying to assume that the energy $E$ is a very small negative number, solve the Schrodinger equation, and find the suitable value of $a$, but I'm having trouble doing this.

Would someone be able to help me with this problem?

## closed as too localized by dmckee♦Nov 7 '12 at 14:16

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• I would suggest at least finding the bound state and its energy before you try to do anything sexy with limits and such. – DJBunk Nov 5 '12 at 23:43
• Do know how to find the eigenvectors and eigenvalues in a case like this? – DJBunk Nov 6 '12 at 3:09
• I got something for you, give me a minute – Dylan O. Sabulsky Nov 6 '12 at 3:14

Consider the double delta-function potential $$V(x)=-\alpha[\delta(x+a)+\delta(x-a)]$$ where $a$ and $\alpha$ are positive constants.    Hope this helps! -Dylan