The eigenvalue moment method (EMM) is a precise technique for generating converging lower and upper bounds to the low-lying eigenenergies of singular quantum Hamiltonians. We apply it to the quartic anharmonic double-well oscillator problem, ${\mathit{P}}^2$-${\mathit{Z}}^2$${\mathit{x}}^2$+${\mathit{x}}^4$, recently studied by Saavedra and Buendia [Phys. Rev. A 42, 5073 (1990)]. In addition, we introduce important algorithmic modifications to the conventional EMM formulation, leading to more efficient applications.

• Received 11 October 1991

DOI:https://doi.org/10.1103/PhysRevA.46.1663