An accurate spectral method for solving the Schroedinger equation
msra(2002)
摘要
The solution of the Lippman-Schwinger (L-S) integral equation is equivalent
to the the solution of the Schroedinger equation. A new numerical algorithm for
solving the L-S equation is described in simple terms, and its high accuracy is
confirmed for several physical situations. They are: the scattering of an
electron from a static hydrogen atom in the presence of exchange, the
scattering of two atoms at ultra low temperatures, and barrier penetration in
the presence of a resonance for a Morse potential. A key ingredient of the
method is to divide the radial range into partitions, and in each partition
expand the solution of the L-S equation into a set of Chebyshev polynomials.
The expansion is called "spectral" because it converges rapidly to high
accuracy. Properties of the Chebyshev expansion, such as rapid convergence, are
illustrated by means of a simple example.
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关键词
integral equation,chebyshev polynomial,spectral method
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