The chemical potential for interacting fermions in a harmonic potential

One of the key concepts in density functional theory is the chemical potential. For a fixed Hamiltonian in second-quantized form one may define a sequence of ground state energies E(N) for varying integral number, N, of electrons. The authors define an equation whereby the energy may be logically regarded as piece-wise linear in N with discontinuities in the slope precisely at the points where mu is sought. Topics discussed include N-body harmonic oscillator, as discussion of the results, and speculation on the chemical potential defined as the derivative of E with respect to natural orbital occupation