  We solve the generalized relativistic harmonic oscillator in 1+1 dimensions,
i.e., including a linear pseudoscalar potential and quadratic scalar and vector
potentials which have equal or opposite signs. We consider positive and
negative quadratic potentials and discuss in detail their bound-state solutions
for fermions and antifermions. The main features of these bound states are the
same as the ones of the generalized three-dimensional relativistic harmonic
oscillator bound states. The solutions found for zero pseudoscalar potential
are related to the spin and pseudospin symmetry of the Dirac equation in 3+1
dimensions. We show how the charge conjugation and $\gamma^5$ chiral
transformations relate the several spectra obtained and find that for massless
particles the spin and pseudospin symmetry related problems have the same
spectrum, but different spinor solutions. Finally, we establish a relation of
the solutions found with single-particle states of nuclei described by
relativistic mean-field theories with scalar, vector and isoscalar tensor
interactions and discuss the conditions in which one may have both nucleon and
antinucleon bound states.
