Monotonicity of quantum ground state energies: Bosonic atoms and stars

The N-dependence of the non-relativistic bosonic ground state energy is studied for quantum N-body systems with either Coulomb or Newton interactions. The Coulomb systems are "bosonic atoms," with their nucleus fixed, and it is shown that grows monotonically in N > 1, where. The Newton systems are "bosonic stars," and it is shown that when the Bosons are centrally attracted to a fixed gravitational "grain" of mass M > 0, and N >2, then grows monotonically in N, where P_N(N) = N (N - 1)(N-2); in the translation-invariant problem (M = 0), it is shown that when N > 1 then grows monotonically in N, with from the Coulomb problem. Some applications of the new monotonicity results are discussed.