The Hulthen potential has the following form:

;

you can adjust the parameter . In the limit as , this reduces to a Coulomb potential . For , the potential simulates a three-dimensional delta function .

Consider the radial Schrödinger equation, in atomic units :

,

in terms of the reduced radial function . The Schrödinger equation can be solved in closed form for -states (). The (unnormalized) solutions are given by

,

where

, ,

In the limit as , the energy approaches the Coulomb value .

Choose "eigenvalues" to show the potential curve in black and the Coulomb potential in red. For each, the energy levels for , and are shown as horizontal lines. Assume . Choose "eigenfunctions" to show plots of the radial functions in black and the corresponding Coulombic (hydrogen atom) functions in red; they merge as is increased.