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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 schr dinger equation

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

Cris Cecka

April 29th 2004

Harvey Mudd College

purpose
Purpose
  • To derive a Numerical Integration method for the One-Dimensional Time-Dependent Schrödinger Equation.
  • To determine validity and accuracy of method.
check it out
Check it Out

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

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

Astounding

future plans
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
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