Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks to the Resonance-Decay Problem in Quantum Mechanics from a
  mathematical point of view   The description of bumps in scattering cross-sections by Breit-Wigner
amplitudes led in the framework of the mathematical Physics to its formulation
as the so-called Resonance-Decay Problem. It consists of a spectraltheoretical
component and the connection of this component with the construction of
decaying states. First the note quotes a solution for scattering systems, where
the absolutely continuous parts of the Hamiltonians are semi-bounded and the
scattering matrix is holomorphic in the upper half plane. This result uses the
approach developed by Lax and Phillips, where the energy scale is extended to
the whole real axis. The relationship of the spectraltheoretical part of its
solution and corresponding solutions obtained by other approaches is explained
in the case of the Friedrichs model. A No-Go theorem shows the impossibility of
the total solution within the specific framework of non-relativistic quantum
mechanics. This points to the importance of the Lax-Phillips approach. At last,
a solution is presented, where the scattering matrix is meromorphic in the
upper half plane.

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org