Cris Cecka April 29th 2004 Harvey Mudd College A Real-Time Numerical Integrator for the One-Dimensional Time-Dependent Schrödinger Equation Cris Cecka April 29th 2004 Harvey Mudd College

Purpose To derive a Numerical Integration method for the One-Dimensional Time-Dependent Schrödinger Equation. To determine validity and accuracy of method.

It’s all Greek…

A whole lotta Greek

Almost there…

Sweet

Check it Out http://www.cs.hmc.edu/~ccecka/QuantumModel

Accuracy Baby

Other Tests

Other Other Tests The eigenfunction expansion of the wave form can be shown to be conserved over long periods!! Astounding

Future Plans User defined potential Time-Dependent potential Dirac Smashing Mathematical implication of complex-valued potentials Momentum space Derivation of eigenfunction expansion using interference patterns

References A. Askar and A.S. Cakmak, Explicit Integration Method for the Time-Dependent Schrodinger. Equation for Collision Problems, J. Chem. Phys. (1978). Visscher, P. B. A fast explicit algorithm for the time-dependent Schrodinger equation. Robert Eisberg and Robert Resnick, Quantum Physics (John Wiley \& Sons, Inc., New York, 1974) L. G. de Pillis, private communcation, 2004