  An exact analytical solution is derived for the wavefunction of an electron
in a one-dimensional moving quantum dot in a nanowire, in the presence of
time-dependent spin-orbit coupling. For cyclic evolutions we show that the spin
of the electron is rotated by an angle proportional to the area of a closed
loop in the parameter space of the time-dependent quantum dot position and the
amplitude of a fictitious classical oscillator driven by the time-dependent
spin-orbit coupling. By appropriate choice of parameters, we show that
arbitrary spin rotations may be performed on the Bloch sphere. Exact
expressions for dynamical and geometrical phases are also derived.
