Concavity Properties of Energy Levels as Functions of Angular Momentum and Level Spacing

Abstract

We prove that the ground-state energy in a central potential is a concave (convex) function of the angular momentum l, if the potential is a concave (convex) function of r2. We then deduce that the ground-state energy of angular momentum l + 1 is larger (smaller) than the average of the energies of the ground state and first radially excited state of angular momentum l, if the potential is concave (convex) in r2. Generalizations to higher radial excitations are discussed.