  We have analytically studied bound states of the one-dimensional Dirac
equation for scalar and vector double square-well potentials (DSPs), by using
the transfer-matrix method. Detailed numerical calculations of the eigenvalue,
wave function and density probability have been performed for the three cases:
(1) vector DSP only, (2) scalar DSP only, and (3) scalar and vector DSPs with
equal magnitudes. We discuss the difference and similarity among results of the
cases (1)-(3) in the Dirac equation and that in the Schr\"{o}dinger equation.
Motion of a wave packet is calculated for a study on quantum tunneling through
the central barrier in the DSP.
