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

Abstract

We compute the energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the the electron is confined. With the help of a mixed-basis variational method we compute the wave function and the energy level and show how it depends on the magnetic field strength. We compare the results with those obtained numerically as well as in the non-relativistic limit.

The Energy Eigenvalues of the Two Dimensional Hydrogen Atom in a Magnetic Field

“…The solution of this problem is very interesting and popular because of the technological advances in nanofabrication technology which has enabled the creation of low-dimensional structures such as quantum wires, quantum dots and quantum wells in semiconductor physics. Recent developments in nanostructure technology has also permitted one to study the behavior of electrons and impurities in quasi two-dimensional configurations (quantum wells) [1,2,3,4,5,6,7,8,9,10,11].…”

Energy spectrum of a 2D Dirac oscillator in the presence of a constant magnetic field and an antidot potential

“…This replacement was proposed by Moshinsky and Szczepaniak [11]. It has been applied for several problems in hadron spectroscopy [19,20], in quark confinement, in broken symmetries [21,22] and in semiconductor physics [23].in the investigation of the thermodynamic properties of some physical potentials [24], The interaction with the magnetic field is introduced by means of the minimal substitution…”

Charge currents and induced magnetic fields in a bounded two-dimensional hydrogen atom

“…Soylu and Boztosun have presented the energy eigenvalues of a twodimensional hydrogenic donor in a magnetic field by using the asymptotic iteration method [23]. The energy spectrum of the ground state of a 2D Dirac electron in the presence of a Coulomb potential and a constant magnetic field perpendicular to the plane where the a e-mail: shalini lumb@hotmail.com b e-mail: sonia lumb@hotmail.com c e-mail: vprasad@ss.du.ac.in (corresponding author) electron is confined has been computed with the help of a mixed-basis variational method by Villalba et al [24].…”