| Abstract: | I will present our recent results where the spectral properties of one-dimensional Dirac Hamiltonian were examined by both qualitative and quantitative methods. We will discuss sufficient conditions for existence of bound states in the spectrum of Dirac Hamiltonian with asymptotically constant vector potential. These results are complemented by quantitative approach where the technique of intertwining operators (Crum-Darboux transformation) is utilized to construct exactly solvable models. Possible application of the results is discussed in the context of condensed matter systems, e.g. graphene of carbon nanotubes |
