Energy States of Two Electrons in a Parabolic Quantum Dot in a Magnetic Field

Abstract

Trie energy spectra of two interacting electrons in a quantum dot confined by a parabolic potential in an applied magnetic field of arbitrary strength are obtained. The shifted 1/N expansion method is used to solve the effective-mass Hamiltonian. Trie influence of the electron-electron interaction on the ground-state energy and its significant effect on the energy level-crossings in states with different angular momenta is shown. Trie dependence of the ground-state energy on trie magnetic field strength for various confinement energies is presented. Comparisons show that our calculated spectra of the quantum dot states are m good agreement with different works. 1.

Energy Spectra of Two Particles in a Parabolic Quantum Dot: Numerical Sweep Method

“…Different methods have been used to solve the problem for D 2: variational [25], power series [12], shifted 1aN expansion [14], exact diagonalization [16,17], or numerical [20]. In this article we propose to use the trigonometric sweep method [27], which as compared with the mentioned above gives a more stable algorithm to obtain numerical solutions for 2D and 3D two electrons and electron±hole pair in QD.…”

“…The two-dimensional case (D 2) in the presence of the magnetic field perpendicular to the plane where the particles are restricted to move is of special interest. In this case, the parameter g 0 in formulae (4) and (5) must be replaced by g defined as [14]:…”

“…The energy levels of two electrons in a two-dimensional (2D) spherical quantum dot (SQD) with parabolic potential were obtained by using Taylor [12] and renormalized perturbation [13] series, shifted 1/N expansion method [14], interpolation formula [15] and the exact numerical methods [16 to 18]. The energy levels of a two-electron quantum disk with rectangular and parabolic potentials as a function of external magnetic field were analyzed by using numerical analysis [19].…”

SWKB formalism for confined quantum systems

“…Since compression of an atom gives rise to very subtle effects, the corresponding Schrödinger equation is generally not solvable analytically for such systems of physical interest. Consequently, one has to take recourse to different approximation methods, e.g., the direct variational method [6,7], the shifted 1/N expansion procedure [3,8], the phaseintegral (WKB) approximation [1,2], etc., or else settle down for a numerical solution. Of the various approximation techniques applied to numerous problems in physics, the semiclassical WentzelKramers-Brillouin (WKB) method is highly successful in estimating the energy spectrum of the system [9,10].…”

Two-Electron Ground State Instabilities in Small Quantum Dots

“…For this model the investigators have been used several approaches: quantum Monte Carlo techniques [6], Taylor and renormalized perturbation series [7,8], shifted 1/N expansion method [9], and exact numerical methods [10][11][12][13]. The instability of the ground state electronic structure with respect to increasing magnetic field strength has been found for this model [9][10][11][12][13]. Other types instabilities of the ground state of the system of many interacting electrons placed in QDs have been discussed in Refs.…”