Solving the MF equations even for a single particle in a inhomogeneous setting (a single electron on some ionic background) is not analytically feasible. Instead introduced the insight of using Linear Combination of Atomic Orbitals (LCAO). Atomic orbitals are spherically symmetric and analytic functions, Roothaan's insight is that they may be added together to capture the inhomogeneous aspects of molecular-orbitals (lack of spherical or rotational symmetry). This may done by a rotation matrix A α p :