Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Green's functions for Hamiltonians with potentials possessing
  singularity at the origin: application to the zero-range potential formalism   We evaluate the short-range asymptotic behavior of Green's function for a
Hamiltonian when its potential energy part has an inverse power singularity at
the origin. The analytically solvable case of sharply screened Coulomb
potential is considered firstly. For this potential the additional logarithmic
singular term has been found in the short-range asymptote of the Green function
as in the case of the pure Coulomb potential. The case of a short-range
potential of an arbitrary form with inverse power singularity is treated on the
basis of the integral Lippmann-Schwinger equation. It is shown that, if the
singularity is weaker than the Coulomb one, the Green function has only
standard singularity. For the case of $r^{-\rho}$ singularity of the potential
with $1\le\rho<2$ the additional singularity in the asymptotic behavior of the
Green function appears. In the case of $\rho=1$ the additional logarithmic
singularity has the same form as in the case of the pure Coulomb potential. In
the case of $1<\rho<2$ the additional singularity of the Green function has the
form of the polar singularity $r^{-\rho+1}$. These results are applied for
extending the zero-range potential formalism on Hamiltonians with singular
potentials.

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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
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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: solv-int
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom