This is the second part of our work dealing with spectral analysis for the Hamiltonian of
three identical one-dimensional quantum particles. The Hamiltonian is represented as a sum of Laplacian
and a singular delta-potential with the symmetric support consisting of six half-lines (leads)
with the same origin. Contrary to the first part discussing the discrete spectrum and the eigenfunctions,
the second part is devoted to study of the negative essential spectrum and the corresponding
generalized eigenfunctions. It turns out that, instead of the Kontorovich–Lebedev integral representation
exploited for the eigenfunctions of the discrete spectrum, alternative integral representations
of the Watson–Bessel type for the generalized eigenfunctions of the essential spectrum are applied.
As in the first part, the symmetry of the support of the corresponding singular potential is made
use of. The operator is decomposed to the fibers by means of the Fourier transform on the group of
symmetry. Further analysis is connected with the investigation of the problem for the fibers and leads
to the study of spectral properties of a functional equation similar to that for the Maryland model.
The results obtained here enable one to determine explicit formulas for the generalized eigenfunction
and to study their behavior at far distances by means of reduction to the Sommerfeld integral representations.
The far field asymptotics of the generalized eigenfunctions are interpreted as surface waves
localized near the leads of the support of the singular potential.