Quantum Computation by Sums of Classical Trajectories

Dr. Robert Manning, Williams College

Explicit solution of quantum mechanical problems involves solution of the initial-value problem for a partial differential equation. However, in certain limits, easier methods are available to produce approximate solutions to the quantum problems. A common example involves reducing the p.d.e. solution to a sum over solutions of a corresponding system of o.d.e.'s.

We illustrate the implementation of such sum-over-trajectories computations by means of several one-degree-of-freedom examples. In addition, we discuss computational issues which arise in applying the methods to more complicated problems.