Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mathematical predominance of Dirichlet condition for the one-dimensional
  Coulomb potential   We restrict a quantum particle under a coulombian potential (i.e., the
Schr\"odinger operator with inverse of the distance potential) to three
dimensional tubes along the x-axis and diameter $\varepsilon$, and study the
confining limit $\varepsilon\to0$. In the repulsive case we prove a strong
resolvent convergence to a one-dimensional limit operator, which presents
Dirichlet boundary condition at the origin. Due to the possibility of the
falling of the particle in the center of force, in the attractive case we need
to regularize the potential and also prove a norm resolvent convergence to the
Dirichlet operator at the origin. Thus, it is argued that, among the infinitely
many self-adjoint realizations of the corresponding problem in one dimension,
the Dirichlet boundary condition at the origin is the reasonable
one-dimensional limit.

23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th