  We examine the performance of various time propagation schemes using a
one-dimensional model of the hydrogen atom. In this model the exact Coulomb
potential is replaced by a soft-core interaction. The model has been shown to
be a reasonable representation of what occurs in the fully three-dimensional
hydrogen atom. Our results show that while many numerically simple (low order)
propagation schemes work, they often require quite small time-steps. Comparing
them against more accurate methods, which may require more work per time-step
but allow much larger time-steps, can be illuminating. We show that at least in
this problem, the compute time for a number of the more accurate methods is
actually less than lower order schemes. Finally, we make some remarks on what
to expect in generalizing our findings to more than one dimension.
