  We give a method for obtaining states of massive particle representations of
the two-parameter deformation of the Poincar\'e algebra proposed in
q-alg/9601010, q-alg/9505030 and q-alg/9501026. We discuss four procedures to
generate eigenstates of a complete set of commuting operators starting from the
rest state. One result of this work is the fact that upon deforming to the
quantum Poincar\'e algebra the rest state is split into an infinite number of
states. Another result is that the energy spectrum of these states is discrete.
Some curious residual degeneracy remains: there are states constructed by
applying different operators to the rest state which nevertheless are
indistinguishable by eigenvalues of all the observables in the algebra.
