Numerical solution to the Schrödinger equation by constrained optimization Free

The nonlinear optimization techniques of dynamic simulated annealing and steepest descents make it feasible to solve numerically the Schrödinger equation for systems that have many degrees of freedom. These methods involve finding the solution to a set of quasi‐Newtonian equations of motion derived from a fictitious, time‐dependent Schrödinger equation. The formalism is reviewed and the methods are illustrated by solving the Schrödinger equation for three simple models: a two‐state system, an infinite square well, and the Mathieu equation.