  For an electrically driven electron confined in a nanowire quantum dot with
spin-orbit coupling (SOC), we find a SOC-magnetism phase-locked condition under
which we derive a complete set of Schr\"odinger kitten states which contains
some novel degenerate ground states with oscillating wave packets or stationary
double packets in undriven case. We identify such wave packets as Majorana-like
quasiparticles and demonstrate that they obey non-Abelian statistics and behave
similarly to neutral particles. The braiding operations based on the
interchanges of the degenerate non-Abelian quasiparticles are shown, which
shift the system between different ground states and may be insensitive to
perturbations and weak noise from the environment. The results could be tested
experimentally in the existing setups and could be treated as the leading-order
results to directly extended to an array of weakly coupled single-electron
quantum dots for topological quantum computation.
