  We theoretically study trapped one-dimensional Fermi gases in the presence of
spin-orbit coupling induced by Raman lasers. The gas changes from a
conventional (non-topological) superfluid to a topological superfluid as one
increases the intensity of the Raman lasers above a critical chemical-potential
dependent value. Solving the Bogoliubov-de Gennes equations self-consistently,
we calculate the density of states in real and momentum space at finite
temperatures. We study Majorana fermions (MFs) which appear at the boundaries
between topologically trivial and topologically non-trivial regions. We
linearize the trap near the location of a MF, finding an analytic expression
for the localized MF wavefunction and the gap between the MF state and other
edge states.
