Variational approach to quasi-two-dimensional hydrogenic impurities in arbitrary magnetic fields

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

“…The Hamiltonian in Ref. [18,19] contains this term and therefore the energy spectrum depends on the dimensions of the confining well. Since the variational technique applied in this paper is equivalent to the method suggested by Chen et al [18,19], our results reduce, in the non relativisic limit, and when the width of the well is negligible, to those reported by Chen et al Finally we mention that s states are not present for the 2D Klein-Gordon Hydrogen atom.…”

“…[18,19]. Here the authors consider a non relativistic quasi two-dimensional system confined by a square-well V B (z).…”

“…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…”

“…Using a mixed-basis variational approach [18,19]. In Sec 2, we compute the relativistic energy spectrum of a 2D relativistic Klein-Gordon hydrogen atom.…”

Anisotropic features of two-dimensional hydrogen atom in magnetic field

“…Initially, the 2D model of the hydrogen atom was investigated within purely theoretical considerations [7][8][9][10], but it was also applied to describe highly anisotropic three-dimensional crystals [11]. With the development of experimental methods for creation of low-dimensional systems and new prospects for development of semiconductor devices, the 2D hydrogen model was used to describe the effect of a charged impurity in 2D systems [12][13][14] and effective interaction in the exciton electron-hole pair, the motion of which is limited by the plane, in semiconductor 2D heterostructures [15]. A number of studies investigated the internal symmetries of the model and the reasons for accidental degeneracy occurring in the three-dimensional (3D) case as well [15][16][17].…”