Let V(x)=−uδ(x)−vδ(x−a) where u,v>0 correspond to a potential with two δ wells. Let v>u. If a is very large, there is certainly a bound state: the particle sits in the δ-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?
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