Relativistic spectral comparison theorem in two dimensions

Abstract

We demonstrate a spectral comparison theory for the two-dimensional Dirac equation which states that for a given mass, if two time-independent attractive potentials are different such that ${V}_{a}l{V}_{b}$, the corresponding energy spectrum satisfies the condition ${E}_{a}l{E}_{b}$. As an illustrative example, the comparison relation is applied to calculate the energy spectrum of the two-dimensional Dirac equation with a Coulomb plus linear potential.