VARIATIONAL METHOD AND THE STOCHASTIC-LIOUVILLE EQUATION .1. FINITE-ELEMENT SOLUTION TO THE CIDN(E)P PROBLEM

A variational formulation is developed for the stochastic-Liouville equation (SLE). It is shown how this formulation may be used as a general basis for the study of numerical and approximate methods of solution of the SLE. The finite element method is developed for the approximate solution of the spin-density matrix elements using the variational formulation. The method is illustrated by employing it to obtain a compact computer-oriented solution to the (high-field) chemically-induced spin polarization problem. This solution is both more efficient as well as more accurate than the previous treatment by Pedersen and Freed using finite difference methods. Various features of finite element and finite difference methods are compared from the viewpoint of this solution. The great flexibility of finite element methods for solution of the SLE is discussed. © 1979 American Institute of Physics.