  We explain the finite as well as infinite degeneracy in the spectrum of a
particular system of spin-1/2 fermions with spin-orbit coupling in three
spatial dimensions. Starting from a generalized Runge-Lenz vector, we
explicitly construct a complete set of symmetry operators, which span a
noncompact SO(3,2) algebra. The degeneracy of the physical spectrum only
involves a particular, infinite, so called singleton representation. In the
branch where orbital and spin angular momentum are aligned the full
representation appears, constituting a 3D analogue of Landau levels.
Anti-aligning the spin leads to a finite degeneracy due to a truncation of the
singleton representation. We conclude the paper by constructing the spectrum
generating algebra of the problem.
