Location of essential spectrum of intermediate Hamiltonians restricted to symmetry subspaces

Abstract

A theorem is presented on the location of the essential spectrum of certain intermediate Hamiltonians used to construct lower bounds to bound‐state energies of multiparticle atomic and molecular systems. This result is an analog of the Hunziker–Van Winter–Zhislin theorem for exact Hamiltonians, which implies that the continuum of an N‐electron system begins at the ground‐state energy for the corresponding system with N−1 electrons. The work presented here strengthens earlier results of Beattie [SIAM J. Math. Anal. 1 6, 492 (1985)] in that one may now consider Hamiltonians restricted to the symmetry subspaces appropriate to the permutational symmetry required by the Pauli exclusion principle, or to other physically relevant symmetry subspaces. The associated convergence theory is also given, guaranteeing that all bound‐state energies can be approximated from below with arbitrary accuracy.