Scaled Variational Computation of the Energy Spectrum of a Two-Dimensional Hydrogenic Donor in a Magnetic Field of Arbitrary Strength

Abstract

We compute the energy levels of a 2D Hydrogen atom when a constant magnetic field is applied. With the help of a mixed-basis variational method and a generalization of virial theorem, which consists in scaling the wave function, we calculate the binding energies of the 1S, 2P − and 3D − levels. We compare the computed energy spectra with those obtained via a generalization of the mesh point technique as well as the shifted 1/N method. We show that the variational solutions present a very good behavior in the weak and strong magnetic field regimes.

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].…”

A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

“…Differing from the single-electron model [5], for a 2D magnetically trapped electron-pair both the Coulomb and harmonic potentials work simultaneously and the exact solutions of the system depend on some particular values of the harmonic oscillator frequency determined by the magnetic field intensity [26][27][28][29][30][31]. In this paper we apply the exact results to a 2D magnetically trapped electronic gas and seek its level structure that consists of the degenerate lowest Landau level of center-of-mass motion and the non-degenerate energy band-likes of relative motion based on the electron-pairs.…”

“…It is important to note that such a dimensionality exists in the quantum Hall systems. We also notice that a 2D electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic field [26][27][28][29][30][31], which represents stable stationary states of the system. On the other hand, the relations between Hall effects and analytical solutions of some quantum systems have been investigated recently [32,33].…”

Calculation of the energy spectrum of a two-electron spherical quantum dot

“…In order to establish the accuracy of the results obtained by the application of the shifted 1/N method we compare them with those obtained by using the Schwartz's numeric method [19]. The method is based in a numerical approximation of functions on a mesh and gives very accurate results [20,21]. There are only empirical estimates of the error [19] which turns out to be exponentially decaying with the number of points given the mesh step.…”