Two-Dimensional Hydrogen-like Atom: Photon Emission and Relativistic Energy Corrections

Abstract

Using the well-known solution Ψ_S of the Schrödinger equation for an electron in the field of a nucleus (Ze) in polar coordinates, via which the spin-state-dependent Dirac spinor Ψ_± obtained here is expressed, and by extending the QED methods to subspace {0; 1, 2}, we have calculated the probability of single-photon emission by a two-dimensional hydrogen-like atom with allowance made for the polarization and spin states. Relativistic energy corrections ∼(Zα)⁴ to the energy value have also been found. We show that the so-called contact interaction typical of a three-dimensional hydrogen-like atom also takes place in the twodimensional case, while the ordinary three-dimensional spin–orbit interaction is absent altogether.