Complex partition function of 1-dimensional Dirac particle confined in Woods-Saxon interaction

We present the bound state solutions of one-dimensional Schr"{o}dinger and Dirac equations for a particle confined in Woods-Saxon potential. In each case the wavefunctions and the energy eigenvalues have been obtained in terms of the Jacobi polynomials by using the Nikiforov-Uvarov method. The complex eigenenergy obtained from the Dirac equation is explicitly shown to contain the nonrelativistic energies plus complex relativistic correction terms. The quantum partition functions obtained using the relativistic and the nonrelativistic energies have been used to generate important thermodynamic properties of the system in the high temperature limit. In particular, the complex partition function obtained in the relativistic regime is taken to indicate some important physical effects in the system.