Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Introduction to Scattering Theory   The purpose of these lectures is to give an accessible and self contained
introduction to quantum scattering theory in one dimension. Part A defines the
theoretical playground, and develops basic concepts of scattering theory in the
time domain (Asymptotic Condition, in- and out- states, scattering operator
$\hat{S}$). The aim of Part B is then to build up, in a step-by-step fashion,
the time independent scattering theory in energy domain. This amounts to
introduce the Lippmann-Schwinger equation for the stationary scattering states
(denoted as $| \psi_{E(\pm 1)}^\pm \rangle$), to discuss fundamental properties
of $| \psi_{E(\pm 1)}^\pm \rangle$, and subsequently to construct $\hat{S}$ and
$\hat{T}$ operators in terms of $| \psi_{E(\pm 1)}^\pm \rangle$. Physical
contents of the $\hat{S}$ and $\hat{T}$ operators is then illuminated by
deriving explicit formulas for the probability of transmission/reflection of
our quantum particle through/from the interaction region of the potential. An
illustrative numerical example is given, which also highlights an existence of
scattering resonances. Finally, Part C elaborates the nonhermitian scattering
theory (Siegert pseudostate formalism), which offers an extremely powerful tool
suitable for clear cut understanding of the resonance phenomena.

2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
16
The categories of this paper are: stat
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat