The laplacian of the potential and the order of energy levels

We prove that for non-relativistic two-body systems the order of energy levels with the same principal Coulomb quantum number is controlled by the sign of the laplacian of the (spherically symmetric) potential. If it is positive, the levels with larger angular momentum have lower energy. If it is negative, it is the opposite, but in the latter case a weaker condition can be derived. In numerous situations in particle and nuclear physics as well as atomic and solid state physics, the laplacian has a definite sign. (orig.)