Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spin-1/2 square-root operator equation with Coulomb potential - a
  perturbation analysis   Seeking for a relativistic generalisation of the non-relativistic
Schroedinger equation, one very soon arrives at equations with a square-root
operator by having applied the quantum mechanical correspondence principle to
the formula of relativistic energy. The problems of these equations are at
least two fold: when coupled to an electromagnetic field, their relativistic
invariance is not evident or even doubtful and due to their non-local
character, it seems to be that they cannot be maintained mathematically in an
easy way. For spin-1/2 particles, these difficulties can be overcome by the
Dirac equation, which leads e.g. to the prediction of binding energies of an
electron in a hydrogen atom that are compatible with experimental results up to
the forth order of the fine structure constant, inclusively. Ignoring the
problem with relativistic invariance, one may ask, if there exists a
square-root equation, for which one can achieve the same good agreement with
experiments for the latter physical system. It is going to be shown, that the
answer to this question is affirmative and does not exceed the skills obtained
in a course about non-relativistic quantum mechanics and physics of atoms,
respectively.

6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an