- Time evolution of the wave function ψ(x,t):
- in suitable units given by
- with the Hamilton operator
- where

- in suitable units given by
- Interpretation of ψ:
- normed solutions in L
_{2}(R^{n}) describe a particle, i.e. - probability p(B) to find the particle in region

- normed solutions in L
- Numerical solution:
- finite differences in x and t
- based on algorithm by DeRaedt (4
^{th}order in dx and dt) - "perfectly matched layer" → no boundary reflections