The Pseudospectral Method for the Dirac Equation with Confining Potential

Abstract: We observe that solving the Dirac equation for confined potentials using the generalized pseudospectral (GPS) method leads to deteriorating convergence of energy eigenvalues and highly oscillatory in wave functions as the confinement radius decreases. It is found that this issue stems from the first-order differentiation formulation employed in GPS method. Motivated by this insight, we adopt the kinetically balanced generalized pseudospectral method, which incorporates the kinetically-balanced condition into the GPS method. Numerical results demonstrate that the mono-kinetically-balanced generalized pseu dospectral (MKB-GPS) method yields converged energy eigenvalues and generates smooth, continuous wave functions. This is the first application of the MKB-GPS method to confined potentials, and its effectiveness is validated for small confinement radii.