▎ 摘　　要

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.