  We derive one-dimensional effective Hamiltonians for spin-orbit coupled Fermi
gases confined in quasi-one-dimensional trapping potentials. For energy regime
around the two-body bound state energy, the effective Hamiltonian takes a
two-channel form, where the population in transverse excited levels are
described by dressed molecules in the closed channel. For energy regime
slightly above the continuum threshold, the effective Hamiltonian takes a
single-channel form, where low-energy physics is governed by the
one-dimensional interacting strength determined by three-dimensional scattering
length and transverse confinement. We further discuss the effect of spin-orbit
coupling and effective Zeeman field on the position of confinement-induced
resonances, and show that these resonances can be understood as Feshbach
resonances between the threshold of the transverse ground state and the
two-body bound state associated with the transverse excited states. We expect
that the shift of confinement-induced resonances can be observed under present
experimental technology at attainable temperatures.
