  We present a detailed theoretical investigation of persistent spin helices in
two-dimensional electron systems with spin-orbit coupling. For this purpose we
consider a single-particle effective mass Hamiltonian with generalized
linear-in-k spin-orbit coupling term corresponding to a quantum well grown in
an arbitrary crystallographic direction, and derive the general condition for
the formation of the persistent spin helix. This condition applied for the
Hamiltonians describing quantum wells with different growth directions
indicates the possibility of existence of the persistent spin helix in a wide
class of 2D systems apart from [001] model with equal Rashba and Dresselhaus
spin-orbit coupling strengths and the [110] Dresselhaus model. In addition, we
employ the translation operator formalism for analytical calculation of
space-resolved spin density and visualization of the persistent spin helix
patterns.
