Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accurate numerical solutions of the time-dependent Schr\"odinger
  equation   We present a generalization of the often-used Crank-Nicolson (CN) method of
obtaining numerical solutions of the time-dependent Schr\"odinger equation. The
generalization yields numerical solutions accurate to order $(\Delta x)^{2r-1}$
in space and $(\Delta t)^{2M}$ in time for any positive integers $r$ and $M$,
while CN employ $r=M=1$. We note dramatic improvement in the attainable
precision (circa 10 or greater orders of magnitude) along with several orders
of magnitude reduction of computational time. The improved method is shown to
lead to feasible studies of coherent-state oscillations with additional
short-range interactions, wavepacket scattering, and long-time studies of
decaying systems.

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The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga