1. 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

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

3. It’s all Greek…

4. A whole lotta Greek

5. Almost there…

6. Sweet

7. Check it Out

8. Accuracy Baby

9. Other Tests

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

11. 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

12. 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