Lower bounds to the binding energies of td micro.

Abstract

We present lower bounds to the binding energies of the three-body Coulomb system, which were drawn from Rayleigh-Ritz variational upper bounds to the inverse of the Hamiltonian. The method is shown to generalize Temple's lower bound [Proc. R. Soc. London Ser. A 119, 276 (1928)]. We applied the method to eigenvalues of the muonic molecular ion td${\mathrm{\ensuremath{\mu}}}^{+}$ where we reached accuracies of ${10}^{\mathrm{\ensuremath{-}}5}$ natural atomic units or better.