Introduction

Propagation of wavepackets in time means application of the operator

$$\widehat{U}=\widehat{T}e^{-\frac{i}{\hbar }\int\limits _{t_{s}}^{t_{e}}\widehat{H}(t)\mathrm{d}t}$$

to a given wavefunction $\psi (t=t_{a}=0)$ to obtain the state of the system at a later time. Trying to simulate the time evolution of a wavepacket, several problems arise:

• representation of the wavefunction on the computer,
• evaluation of the operator $\widehat{H}$,
• approximation of the exponential of an operator.

This article is meant to introduce and classify a few typical techniques which solve these problems and enable the reader to choose or derive the technique which is best suited to his or her problem.