  In this contribution we present some results on the study of pseudospin
symmetry (PSS) in single particle resonant states. The PSS is a relativistic
dynamical symmetry connected with the small component of the nucleon Dirac wave
function. Many efforts have been made to study this symmetry in bound states.
We recently gave a rigorous justification of the PSS in single particle
resonant states by examining the zeros of Jost functions corresponding to the
small components of the radial Dirac wave functions and phase shifts of
continuum states [1, Phys. Rev. Lett. 109 (2012) 072501]. We have shown that
the PSS in single particle resonant states in nuclei is conserved when the
attractive scalar and repulsive vector potentials have the same magnitude but
opposite sign. Examples of exact conservation and breaking of this symmetry in
single particle resonances are given for spherical square-well and Woods-Saxon
potentials.
