  There exists a large class of quantum many-body systems of
Calogero-Sutherland type where all particles can have different masses and
coupling constants and which nevertheless are such that one can construct a
complete (in a certain sense) set of exact eigenfunctions and corresponding
eigenvalues, explicitly. Of course there is a catch to this result: if one
insists on these eigenfunctions to be square integrable then the corresponding
Hamiltonian is necessarily non-hermitean (and thus provides an example of an
exactly solvable PT-symmetric quantum-many body system), and if one insists on
the Hamiltonian to be hermitean then the eigenfunctions are singular and thus
not acceptable as quantum mechanical eigenfunctions. The standard
Calogero-Sutherland Hamiltonian is special due to the existence of an integral
operator which allows to transform these singular eigenfunctions into regular
ones.
