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The Agmon spectral function for molecular hamiltonians with symmetry restrictions

In this paper we introduce symmetry considerations into our earlier work, which was concerned with geometric spectral properties of Schrödinger operators including the N-body operators of quantum mechanics. The point of emphasis is a function introduced by Shmuel Agmon which we have named the Agmon spectral function. We show that this function is symmetric for an N-body Schrödinger operator restricted to a subspace of prescribed symmetry. We then show how it can be used to obtain criteria for the finiteness and infiniteness of bound states of polyatomic systems.