Author: Matchonov, Kuvonchbek Pulat ugli

Annotation: In this article one-dimensional relativistic atoms is studied for confined (in a one-dimensional box) and unconfined cases using the Dirac equation. We obtain the exact solution for the energy spectrum of the hydrogen-like atom which must be determined via solutions to transcendental equations via shifted Coulomb potential and the wave functions expressed in terms of Whittaker functions.

Keywords: Single-particle Dirac Hamiltonian, one-dimensional box, shifted Coulomb potential, Whittaker equation, Dirac matrices, eigenvalues, boundary condition, unitary transform, continuity condition, energy spectra.

Pages in journal: 364 - 370