The relevant Schrödinger equation is given by , in units with , and in bohrs, and in hartrees. For , the equation has separable continuum solutions , where the are spherical harmonics. The radial function has the form for and for . Here and are spherical Bessel functions and the are phase shifts. For each value of , a single bound state will exist, provided that . The bound-state radial function is , where and are the greater and lesser of and , and is a Hankel function. The energy is given by , with determined by the transcendental equation . Both the bound and continuum wavefunctions are continuous at but have discontinuous first derivatives. The produces a deltafunction in the second derivative.

This Demonstration shows plots of the radial functions and a cross section of the density plots of for . The wavefunction is positive in the blue regions and negative in the white regions. Be cautioned that the density plots might take some time to complete.