Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The splitting in potential Crank-Nicolson scheme with discrete
  transparent boundary conditions for the Schr\"odinger equation on a
  semi-infinite strip   We consider an initial-boundary value problem for a generalized 2D
time-dependent Schrodinger equation (with variable coefficients) on a
semi-infinite strip. For the Crank-Nicolson-type finite-difference scheme with
approximate or discrete transparent boundary conditions (TBCs), the Strang-type
splitting with respect to the potential is applied. For the resulting method,
the unconditional uniform in time $L^2$-stability is proved. Due to the
splitting, an effective direct algorithm using FFT is developed now to
implement the method with the discrete TBC for general potential. Numerical
results on the tunnel effect for rectangular barriers are included together
with the detailed practical error analysis confirming nice properties of the
method.

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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci