Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The propagator for the step potential and delta function potential using
  the path decomposition expansion   We present a derivation of the propagator for a particle in the presence of
the step and delta function potentials. These propagators are known, but we
present a direct path integral derivation, based on the path decomposition
expansion and the Brownian motion definition of the path integral. The
derivation exploits properties of the Catalan numbers, which enumerate certain
classes of lattice paths.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th