Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase-amplitude formalism for ultra-narrow shape resonances   We apply Milne's phase-amplitude representation [W. E. Milne, Phys. Rev. 35,
863 (1930)] to a scattering problem involving disjoint classically allowed
regions separated by a barrier. Specifically, we develop a formalism employing
different sets of amplitude and phase functions --- each set of solutions
optimized for a separate region --- and we use these locally adapted solutions
to obtain the true value of the scattering phase shift and accurate tunneling
rates for ultra-narrow shape resonances. We show results for an illustrative
example of an attractive potential with a large centrifugal barrier.

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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex