Lower bounds to ground-state eigenvalues

A new lower bound method is presented for ground-state eigenvalues which relies on the Eckart inequality. The method bears similarity to the variational method and the Temple lower bound formula. Restrictions are that an exactly soluble base Hamiltonian must be available with a positive-semidefinite perturbation to the Hamiltonian of interest. A sample calculation shows that our method is able to sometimes best the Temple bound and also perform rigorously when the Temple bound does not.