Electron in the field of a molecule with an electric dipole moment

In solving the eigenvalue wave equation, we relax the usual diagonal constraint on its matrix representation by allowing it to be tridiagonal. This results in a larger representation space that incorporates an analytic solution for the noncentral electric dipole pole potential cos θ/r2, which was believed not to belong to the class of exactly solvable potentials. Consequently, we obtain closed form solution of the time-independent Schrödinger equation for an electron in the field of a molecule treated as a point electric dipole.