The multigrid method for accelerated solution of the discretized Schrödinger equation

The use of the new multigrid method for the numerical solution of the discretized Schrödinger equation is discussed. A simple approach is chosen to circumvent the difficulties associated with the fact that the Schrödinger differential operator is not positive definite. The scheme is applied to a two-dimensional model problem which includes the essential features present in actual scattering problems. The results show that significant savings can be achieved both in computational work and core memory requirements. The multigrid method should greatly increase the utility of meshing procedures for solving the partial differential equations of quantum mechanics.