Comparison of a Hartree, a Hartree-Fock, and an exact treatment of quantum-dot helium

Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots

“…For general values of this quantity a numerical treatment is required. As mentioned above, the most straightforward one is an integration of the radial equation 7,15 but, nevertheless, other methods such as diagonalization in a basis 16,17 and the Monte Carlo method 18,19 have also been applied. One of us has used the so-called oscillator representation method, perturbatively treating the residual interaction, to derive analytical expressions for the energy levels.…”

Voltage-tunable singlet-triplet transition in lateral quantum dots

“…From the theoretical side, numerical analyses of the interacting two-electron 17,18,19 problem, as well as higher electron numbers, 19,20 demonstrated singlet-triplet transitions in parabolic potentials using either a fixed or an N -dependent harmonic frequency. These works focused on magnetic-field-induced transitions.…”

Coupling and dissociation in artificial molecules

“…As a result, in the last few years, an intensive theoretical effort [1,2,3,4,5,6,7,8,9,10] has been devoted towards the elucidation of the appropriate analogies and/or differences. Recently, we have shown [7,8,9] that, even in the absence of a magnetic field, the most promising analogies are found mainly outside the confines of the central-field approximation underlying the Independent-Particle Model (IPM) and the ensuing physical picture of electronic shells and the Aufbau Principle.…”