My question is do we see in nature any potential which is close to Double Delta Potential barrier/well? If yes then which are those?
Thanks in advance.
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This is often used as a simplified model for a diatomic molecule. Each $\delta$ represents an atom, and the distance between the wells is the nuclear separation.
The solutions can be identified with the so-called bonding and anti-bonding wave functions. The strength parameter for the potential is often set by considering the dissociation regime, i.e. imagining that the two nuclei are so far apart that the electron is trapped in a single $\delta$ well (and - say - setting the binding energy of the one bound state to some known value for the atom).
For instance, when the nuclei are very far apart, the electron sees only one well. Thus, the value of $V_0$ for a model of the $H_2^+$ could be chosen to produce a binding energy of $−13.6$eV in a single isolated $\delta$-well.
This is a fairly common example of many textbooks. If you are interested in published work see: