Bound states of a relativistic spinning particle in an inhomogeneous magnetic field and its thermodynamic properties

The exact solution of the relativistic spinning particle in the inhomogeneous magnetic field is derived. In this approach, the path integral formalism can analytically eliminate the singularity that we encountered in our study at the point y = -1/a, which will give to the kinitic term is a dependent position mass. By using the coordinates transformation, the Green function and the electron propagator are calculated, and the energy eigenvalues and their corresponding eigenfunctions are extracted. The limit case is deduced for a small parameter and the thermodynamic properties are established.