Title tells all. The text inspired by Calogero is well tuned to
his special birthday issue. Review-like recommended reading for
all who love both the S. Lie's symmetries-employing approach to
differential equations and quantum theory. This time, the key
motivation seems to be the fascination by the latter, with shared
(and inspiring) characteristic of the three analyzed examples (for
which, basically, solutions are being derived and discussed) being
the presence of a strong singularity in the origin (which is, by
my opinion, one of the best textbook problems popularized by the
presence of the centrifugal term in radial Schroedinger equations,
well understood via the mathematical Hilbert-space-operator theory
of self-adjoint extensions and revitalized recently in the so
called PT-symmetric analytic-continuation context). The authors
show, compactly and very nicely, how this type of singularities
lives its independent life in the Liean solution-generating
context.


MR2117167
Andriopoulos, K. ; Leach, P. G. L. Some group theoretical aspects of
nonlinear quantal oscillators. J. Nonlinear Math. Phys. 12 (2005),
suppl. 1, 32--42.