Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular Potentials in Quantum Mechanics and Ambiguity in the
  Self-Adjoint Hamiltonian   For a class of singular potentials, including the Coulomb potential (in three
and less dimensions) and $V(x) = g/x^2$ with the coefficient $g$ in a certain
range ($x$ being a space coordinate in one or more dimensions), the
corresponding Schr\"odinger operator is not automatically self-adjoint on its
natural domain. Such operators admit more than one self-adjoint domain, and the
spectrum and all physical consequences depend seriously on the self-adjoint
version chosen. The article discusses how the self-adjoint domains can be
identified in terms of a boundary condition for the asymptotic behaviour of the
wave functions around the singularity, and what physical differences emerge for
different self-adjoint versions of the Hamiltonian. The paper reviews and
interprets known results, with the intention to provide a practical guide for
all those interested in how to approach these ambiguous situations.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci