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

Abstract

We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact Schrödinger, the Hartree-Fock, and the Kohn-Sham equations. The results obtained by applying the shifted-1/N method are compared with those obtained by using an accurate numerical technique, showing that the relative error is reasonably small, although the first method consistently underestimates the correct values. The approximate groundstate Hartree-Fock and local-density Kohn-Sham energies, estimated using the shifted-1/N method, are compared with accurate numerical self-consistent solutions. We make some perturbative analyses of the exact energy in terms of the confinement strength, and we propose some interpolation formulae. Similar analysis is made for both mean-field approximations and interpolation formulae are also proposed for these exchange-only ground-state cases.

A study of two-electron quantum dot spectrum using discrete variable representation method

“…Maybe the most common quantum dot with two interacting electrons is the two-dimensional isotropic harmonic potential. [38][39][40][41] However, many other models have been used, such as the spherical box with finite 42 and infinite [43][44][45][46] walls, the two-dimensional harmonic potential with anharmonic correction, 47 the one-dimensional, 48 square 49,50 and cubic 51,52 boxes with infinite walls, the ellipsoidal quantum dot, 53 the Gaussian confining potential, 54 the two-dimensional anisotropic harmonic potential, 55 and the three-dimensional isotropic [56][57][58][59][60] and anisotropic 61,62 potentials.…”

The Wigner localization of interacting electrons in a one-dimensional harmonic potential

“…First, the confinement due to the harmonic potential can be easily tuned by varying a single parameter. Second, with respect to the other confinement options, the harmonic confinement is more similar to the confinement of electrons in experiments involving homogeneous magnetic fields [54][55][56][57][58] . We focus here on quasi-one-dimensional systems with up to four electrons, which we will allow us to use the very accurate Complete Active Space Self-Consistent Field approach (CASSCF), to study the localization of the electrons.…”

The Ground State Electronic Properties of Two Electron Quantum Dot in External Magnetic and Electric Fields

“…The method is simple, and it gives accurate results of energy eigenvalues calculations of the system without dealing with robust numerical calculations or trail wave functions. The shifted 1/N-expansion method has already been used to study various systems, such as two-dimensional magnetoexcitons (Quiroga, Camacho, & Gonzalez, 1995), shallow donor impurities (El-Said, 1994), two-electron spherical quantum dot (Pino & Villalba, 2001), two interacting electrons in two dimensional quantum dot with the presence of magnetic field (El-Said, 2000;Gomez & Romero, 2009). And recently, we have used the method to calculate energies and binding energies for quantum dot with Gaussian potential confinement (Al-Hayek & Sandouqa, 2015), the results show a very good agreement with other computational methods like asymptotic integration method (AIM) and exact diagonalization method.…”