A NUMERICAL-METHOD FOR FINDING THE GROUND-STATES OF ONE-DIMENSIONAL SYSTEMS

Griffiths and Chou introduced a method of effective potentials for finding the ground states of a class of systems that can be described by classical one-dimensional Hamiltonians with nearest neighbor interactions. In practice the effective potentials must be solved numerically by discretization on a grid of N points. Existing algorithms have calculation times that vary as N2 or worse. We show how this can be reduced to linear in N by means of straightforward optimizations that take advantage of the properties of the effective potentials. © 1990.