Spectroscopic structure of two interacting electrons in a quantum dot by the shifted1/Nexpansion method

Abstract

The shifted 1/N expansion method has been used to study the relative Hamiltonian of two interacting electrons confined in a quantum dot. The eigenenergy spectra are obtained for any arbitrary ratio of Coulomb to confinement energies. Interesting features of the quantum dot spectra, such as the energy-level crossings and the removal of the degeneracy, are explained. Comparisons show that our results are in very good agreement with recent published ones calculated by exact and WKB methods.

N-dimensional electron in an anharmonic potential: The large-N limit

“…We intend to study the efficacy of this expansion method by calculating the energy eigenvalues and showing that to each order of correction, the large-N expansion method always predicts a slightly lower potential as compared to the exact eigenvalue obtained numerically. This is remarkable since this implies a certain monotonicity in these perturbation corrections which tells us that the corrections are always positive, a fact that has often been tacitly assumed in related calculations [16,17]. We argue that this is the underlying reason which makes this method more dynamic compared to standard perturbation technique which is limited strictly to a weak-coupling regime.…”

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.…”

“…Several different approaches have been reported in studying such a system. Exact diagonalization method (Wagner, Merkt, & Chaplik 1992;Merkt, Huser, & Wagner 1991), Hartree and Hartree Fock (HF) Pfannkuche, Gerhats, Maksym, & Gudmundsson, 1993;Palacios, Martin-Moreno, Chiappe, Louis, & Tejedor, 1994), the Monte Carlo calculations (Harju, Sverdlov, & Nieminen 1998;Bolton, 1996), and 1/N expansion method (El-Said, 2000).…”

Magnetic Susceptibility of Coupled Double GaAs Quantum Dot in Magnetic Fields

“…Kandemir [10,11] found the closed form solution for this QD Hamiltonian and the corresponding eigenstates for particular values of the magnetic field strength and confinement frequencies. Elsaid [12][13][14][15][16] used the dimensional expansion technique, in different works, to solve the QD-Hamiltonian and obtain the energies of the two interacting electrons for any arbitrary ratio of Coulomb to confinement energies and gave an explanation to the level crossings. * corresponding author; e-mail: mkelsaid@najah.edu Maksym and Chakraborty [17] implemented the diagonalization method to obtain the eigenenergies of interacting electrons in a magnetic field and show the transitions in the angular momentum of the ground states.…”