Inverted Mexican Hat potential in activation of receptor cells

We consider a potential with two parameters, involving the amplitude and the scale, which adequately represent the real world phenomena concerning the receptor cells in a simple form. This potential also exhibits a sort of “electrical neutrality” making the total effect zero. Mathematically, this requires the potential V(x)=(x2−1)exp(−x2/2)V(x)=(x2−1)exp(−x2/2), satisfy ∫−∞∞V(x)dx=0. It may be seen easily that the exponential decay makes the action of the potential local. This potential function, usually known as Inverted Mexican Hat potential, is found to closely approximate the functioning of bipolar cells in the retina, ion tunneling in ionic channels and also in other neuron cells.