One-dimensional hydrogenic ions with screened nuclear Coulomb field
The study investigates a single electron in a one-dimensional screened Coulomb potential from a nucleus, using the Dirac equation. The analysis shows that the system's energy spectrum is essentially self-adjoint, with a continuous essential spectrum and only finitely many discrete bound states within the gap. These bound states are linked to topological features (heteroclinic saddle-saddle connectors) of an associated dynamical system on a finite cylinder, allowing for a count of bound states based on the nuclear charge.