A LOCAL SOLUTION OF THE SCHRODINGER-EQUATION

A local method is developed for solving the Schrodinger equation. The method is local in the sense that it can determine the value of the so lution of the Schrodinger equation at an arbitrary point directly rath er than extracting this value from the field solution. The method is b ased on properties of diffusion processes, the Ito formula, and Monte Carlo simulation. Simplicity, accuracy, and generality are the main fe atures of the proposed local solution. The extension of the proposed m ethod to solve the stochastic version of the Schrodinger equation is e lementary. Two examples with Dirichlet and Neumann boundary conditions are presented to demonstrate the application and evaluate the accurac y of the proposed local solution.