Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An efficient algorithm based on splitting for the time integration of
  the Schr\"odinger equation   We present a practical algorithm based on symplectic splitting methods to
integrate numerically in time the Schr\"odinger equation. When discretized in
space, the Schr\"odinger equation can be recast as a classical Hamiltonian
system corresponding to a generalized high-dimensional separable harmonic
oscillator. The particular structure of this system combined with previously
obtained stability and error analyses allows us to construct a set of highly
efficient symplectic integrators with sharp error bounds and optimized for
different tolerances and time integration intervals. They can be considered, in
this setting, as polynomial approximations to the matrix exponential in a
similar way as methods based on Chebyshev and Taylor polynomials.
  The theoretical analysis, supported by numerical experiments, indicates that
the new methods are more efficient than schemes based on Chebyshev polynomials
for all tolerances and time intervals. The algorithm we present incorporates
the new splitting methods and automatically selects the most efficient scheme
given a tolerance, a time integration interval and an estimate on the spectral
radius of the Hamiltonian.

36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph