Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization of the strongly attractive inverse square potential:
  Taming the singularity   Quantum anomalies in the inverse square potential are well known and widely
investigated. Most prominent is the unbounded increase in oscillations of the
particle's state as it approaches the origin when the attractive coupling
parameter is greater than the critical value of 1/4. Due to this unphysical
divergence in oscillations, we are proposing that the interaction gets screened
at short distances making the coupling parameter acquire an effective
(renormalized) value that falls within the weak range 0 to 1/4. This prevents
the oscillations form growing without limit giving a lower bound to the energy
spectrum and forcing the Hamiltonian of the system to be self-adjoint.
Technically, this translates into a regularization scheme whereby the inverse
square potential is replaced near the origin by another that has the same
singularity but with a weak coupling strength. Here, we take the Eckart as the
regularizing potential and obtain the corresponding solutions (discrete bound
states and continuum scattering states).

31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ