Analytic solution of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field

Abstract

We obtain exact solutions of the Klein-Gordon and Pauli Schrödinger equations for a two-dimensional hydrogen-like atom in the presence of a constant magnetic field. Analytic solutions for the energy spectrum are obtained for particular values of the magnetic field strength. The results are compared to those obtained in the non-relativistic and spinless case. We obtain that the relativistic spectrum does not present s states.

Energy Spectrum of the Ground State of a Two-Dimensional Relativistic Hydrogen Atom in the Presence of a Constant Magnetic Field

“…This selection gives an overall convergence rate which goes approximately as ≈ 10 (−2/3)N ) where N is the number of truncations. The accuracy of the technique has been verified by computing the energy spectrum of the 2D Hydrogen atom [14][15][16] and reproducing the analytic results obtained by Taut 17 for the excited states. Figure 1 shows the dependence of the non-relativistic energy E − c 2 on the magnetic field strength B.…”

“…11 The non-relativistic two-dimensional Hamiltonian describing the Coulomb interaction −Z/r, between a conduction electron and donor impurity center when a constant magnetic B field is applied perpendicular to the plane of motion has been thoroughly discussed in the literature. [14][15][16][17][18] Despite its simple form, its solutions cannot be expressed in terms of special functions. An analogous situation occurs when we deal with the (2+1) Dirac equation; therefore one has to apply numerical and approximate techniques in order to compute the energy spectrum and the corresponding wave functions.…”

Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength

“…An analogous situation occurs when we use the oscillator basis, in which case we obtain a good agreement for large ω L , but the convergence is very slow for small values of ω L . [23] In order to solve this problem, we propose a trial function [18,19], for any quantum level n, a linear combination of the form…”

Corrigendum to “sl(M+1) construction of quasi-solvable quantum M-body systems” [Ann. Phys. 309 (2004) 239–280]

“…We now can easily integrate the differential equation (4.25) to obtain, 28) where the integral constant is omitted.…”