  Yoram Alhassid conjectured that the total energy of a harmonically trapped
two-component Fermi gas with large scattering length is a linear functional of
the occupation probabilities of single-particle energy eigenstates. We confirm
his conjecture and derive the functional explicitly. We show that the
functional applies to ALL smooth potentials having a minimum, not just harmonic
traps. We also calculate the occupation probabilities of high energy states.
