Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical solutions of the time-dependent Schrodinger equation in two
  dimensions   The generalized Crank-Nicolson method is employed to obtain numerical
solutions of the two-dimensional time-dependent Schrodinger equation. An
adapted alternating-direction implicit method is used, along with a high-order
finite difference scheme in space. Extra care has to be taken for the needed
precision of the time development. The method permits a systematic study of the
accuracy and efficiency in terms of powers of the spatial and temporal step
sizes. To illustrate its utility the method is applied to several
two-dimensional systems.

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The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin