An Improved Lower Bound to the Ground-State Energy

The Arnoldi iterative method for determining eigenvalues is based on the observation that the effect of operating with the Hamiltonian on a vector may be expressed as a sum of parallel and perpendicular contributions. This identity is used here to improve the previous lower-bound estimate of the ground-state energy by Temple, derived 90 years ago [Temple. Proc. Roy. Soc. (London) 1928, A119, 276]. The significantly improved lower bound is exemplified by considering a quartic and a Morse potential. The lower bound is valid for any Hermitian operator whose discrete spectrum is bounded from below.