Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase equivalent potentials, Complex coordinates and Supersymmetric
  Quantum Mechanics   Supersymmetric Quantum Mechanics may be used to construct reflectionless
potentials and phase-equivalent potentials. The exactly solvable case of the
$\lambda sech^2$ potential is used to show that for certain values of the
strength $\lambda$ the phase-equivalent singular potential arising from the
elimination of all the boundstates is identical to the original potential
evaluated at a point shifted in the complex cordinate space. This equivalence
has the consequence that certain general relations valid for reflectionless
potentials and phase-equivalent potentials lead to hitherto unknown identities
satisfied by the Associated Legendre functions. This exactly solvable probelm
is used to demonstrate some aspects of scattering theory.

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The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con
18
The categories of this paper are: econ
16
The categories of this paper are: stat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org