Overview

There is a variety of different propagation schemes for quantum mechanical systems, with different properties. See table 1 for an overview of the methods considered in this article.

Table 1: overview of methods.

method	remarks
Second-order	simple; interaction between potentials;
differencing (SOD)	theoretical considerations
Split operator (SPO)	simple, stable; but no space-momentum
	mixed terms in $\widehat{H}$
Chebyshev	global, long time method;
	exact to computer accuracy
Lanczos	subspace depends on initial state