  The cascade, lambda and vee type of three-level systems are shown to be
described by three different Hamiltonians in the SU(3) basis. We investigate
the Bloch space structure of each configuration by solving the corresponding
Bloch equation and show that at resonance, the seven-dimensional Bloch sphere
${\mathcal S}^7$ is broken into two distinct subspaces ${\mathcal
S}^2{\times}{\mathcal S}^4$ due to the existence of a pair of quadratic
constants. We also give a possible representation of the qutrit wave function
and discuss its equivalence with the three-level system.
