  The problem of localized states in 1D systems with the relativistic spectrum,
namely, graphene stripes and carbon nanotubes, has been analytically studied.
The bound state as a superposition of two chiral states is completely described
by their relative phase which is the foundation of the variable phase method
(VPM) developed herein. Basing on our VPM, we formulate and prove the
relativistic Levinson theorem. The problem of bound state can be reduced to the
analysis of closed trajectories of some vector field. Remarkably, the Levinson
theorem appears as the Poincare indices theorem for these closed trajectories.
The reduction of the VPM equation to the non-relativistic and semi-classical
limits has been done. The limit of the small momentum $p_y$ of the transverse
quantization is applicable to arbitrary integrable potential. In this case the
only confined mode is predicted.
