A linear least-squares variational recipe for the calculation of approximate energy eigenstates

Abstract

The efficacy of the energy-spread minimization technique for solving the energy-eigenvalue equation in a linear variational framework is assessed with a 3×3 matrix perturbation problem with backdoor intruders, quartic anharmonic oscillator and the He-atom problems as prototypical examples. Both direct and indirect minimization schemes are considered and disadvantages of the latter pointed out. The relative merits and demerits of the conventional, vis-a-vis stochastic minimization routes are critically analyzed in the present context.