  Majorana fermions are fascinating and not yet confirmed quasiparticles in
condensed matter physics. Here we propose using microwave spectra to
distinguish Majorana bound states (MBSs) from topological trivial Andreev bound
states. By numerically calculating the transmission and Zeeman field dependence
of the many-body excitation spectrum of a 1D Josephson junction, we find that
the two kinds of bound states have distinct responses to variations in the
related parameters. Furthermore, the singular behaviors of the MBSs spectrum
could be attributed to the robust fractional Josephson coupling and nonlocality
of MBSs. Our results provide a feasible method to verify the existence of MBSs
and could accelerate its application to topological quantum computation.
