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.