  Group-theoretical approach is applied to study behavior of lossless two-level
atoms in a standing-wave laser field. Due to the recoil effect, the internal
and external atomic degrees of freedom become coupled. The internal dynamics is
described quantum mechanically in terms of the SU(2) group parameters. The
evolution operator is found in an explicit way after solving a single ODE for
one of the group parameters. The translational motion in a standing wave is
governed by the classical Hamilton equations which are coupled to the SU(2)
group equations. It is shown that the full set of equations may be chaotic in
some ranges of the control parameters and initial conditions. It means
physically that there are regimes of motion with chaotic center-of-mass motion
and irregular internal dynamics. It is established that the chaotic regime is
specified by the character of oscillations of the group parameter
characterizing the mean interaction energy between the atom and the laser
field. It is shown that the effect of chaotic walking can be observed in a real
experiment with cold atoms crossing a standing-wave laser field.
