Winter model in the quasi-continuum limit
We study Winter or delta-shell model at finite volume (length),
describing a small resonating cavity
weakly-coupled to a large one.
For generic values of the coupling,
a resonance of the usual model corresponds,
in the finite-volume case,
to a compression of the spectral lines;
for specific values of the coupling,
a resonance corresponds instead to a
degenerate or a quasi-degenerate doublet.
A secular term of the form g^3 N
occurs in the perturbative expansion
of the momenta (or of the energies)