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

Abstract

We compute, via a variational mixed-base method, the energy spectrum of a two dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the non-relativistic and spinless case. We find 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.…”

“…For this purpose, we use a two-term mixed-basis variational approach. 16 We also compute the non-relativistic limit with the help of the Pauli equation. Finally, we compare the results with those obtained numerically with the help of the Schwartz method, 19 which is a generalization of the mesh point technique.…”

Relativistic two-dimensional hydrogen-like atom in a weak magnetic field

“…Properties of model two-dimensional hydrogenic systems immersed in a magnetic field have been investigated for several decades within the frameworks of nonrelativistic and relativistic [32][33][34][35][36][37][38][39][40][41][42][43] quantum mechanics. Besides of being interesting from a purely theoretical point of view, results of such studies are also important for understanding various aspects of physics of lowdimensional semiconductors [1][2][3][6][7][8]10,12,15,18,26] and of graphene [44][45][46][47][48][49][50][51].…”

Relativistic Paschen-Back Effect for the Two-Dimensional H-Like Atoms

“…At this stage, the 2D hydrogen problem determines a leading approximation for study of hydrogen type bound states in extreme anisotropic crystals, in which the zcomponent of a diagonal anisotropic mass tensor is much larger than the two remaining ones [4]. The non-and weak-relativistic [5] approaches are usually considered as sufficiently good approximations to the realistic description of the 2D objects in solid matter. However, in a searching of both spin and relativistic effects the complete relativistic theory based on the Dirac equation is inevitable.…”