# What are the real life examples of Double Dirac-Delta Potential barrier/well?

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?

• This post (v1) seems like a list question. Related question by OP: physics.stackexchange.com/q/359747/2451 – Qmechanic Sep 30 '17 at 17:10
• Sorry, but I can't get it. I'm reading from the scratch. Searched over the internet at first, skimmed through books, then posted here. :) The previous question was on the mathematical similarities/dissimilarities. This one about some examples. – Deepayan Turja Sep 30 '17 at 17:13

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:

• Ahmed, Zafar, et al. "Revisiting double Dirac delta potential." Eur. J. Phys 37.045406 (2016): 045406. (arXiv version here.)
• Lapidus, I. Richard. "One-dimensional model of a diatomic ion." American Journal of Physics 38.7 (1970): 905-908 (behind a paywall)
• Could you please explain this part - "setting the binding energy of the one bound state to some known value for the atom"? Also, could you please give references for further reading? (Books would be much preferable.) :) – Deepayan Turja Oct 1 '17 at 8:53
• @DeepayanTurja Added some minor details and references. – ZeroTheHero Oct 1 '17 at 14:16