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A Real-Time Numerical Integrator for the One-Dimensional Time-Dependent Schrödinger Equation

A Real-Time Numerical Integrator for the One-Dimensional Time-Dependent Schrödinger Equation. Cris Cecka April 29 th 2004 Harvey Mudd College. Purpose. To derive a Numerical Integration method for the One-Dimensional Time-Dependent Schrödinger Equation.

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A Real-Time Numerical Integrator for the One-Dimensional Time-Dependent Schrödinger Equation

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  1. 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 http://www.cs.hmc.edu/~ccecka/QuantumModel

  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

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