Solution forms of discretised dirac system with summable and unbounded potentials

Abstract

We have investigated the form of solutions of discretised Dirac system with bounded and unbounded potentials. This we have done using asymptotic summation based on Levinson's theorem. We have shown that the asymptotic behaviour of the matrix solutions of the associated Dirac systems are determined by the dominant corrected eigenvalues depending on the spectral summable parameter in the case of bounded potential and on the dominant corrected eigenvalues depending on the unbounded potential. In both cases, the spectrum of the associated Dirac system is discrete.