  In this paper, we study the massive Dirac equation with the presence of the
Morse potential in polar coordinate. The Dirac Hamiltonian is written as two
second-order differential equations in terms of two spinor wavefunctions. Since
the motion of electrons in graphene is propagated like relativistic fermionic
quasi-particles, then one is considered only with pseudospin symmetry for
aligned spin and unaligned spin by arbitrary $k$. Next, we use the confluent
Heun's function for calculating the wavefunctions and the eigenvalues. Then,
the corresponding energy spectrum obtains in terms of $N$ and $k$. Afterward,
we plot the graphs of the energy spectrum and the wavefunctions in terms of $k$
and $r$, respectively. Moreover, we investigate the graphene band structure by
a linear dispersion relation which creates an energy gap in the Dirac points
called gapped graphene. Finally, we plot the graph of the valence and
conduction bands in terms of wavevectors.
