Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice two-body problem with arbitrary finite range interactions   We study the exact solution of the two-body problem on a tight-binding
one-dimensional lattice, with pairwise interaction potentials which have an
arbitrary but finite range. We show how to obtain the full spectrum, the bound
and scattering states and the "low-energy" solutions by very efficient and
easy-to-implement numerical means. All bound states are proven to be
characterized by roots of a polynomial whose degree depends linearly on the
range of the potential, and we discuss the connections between the number of
bound states and the scattering lengths. "Low-energy" resonances can be located
with great precission with the methods we introduce. Further generalizations to
include more exotic interactions are also discussed.

27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga