Two Electrons in a Quantum Dot: A Unified Approach

Abstract

Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives closed algebraic solutions for the specific values of magnetic field and spatial confinement length, enables us to see explicitly individual effects of the electron correlation.

An extended scenario for the Schrödinger equation

“…where ( ) ( ) f x F g yields an algebraic closed solution for exactly solvable potentials [5][6][7][8][9][10][11][12][13][14][15]…”

“…However, singular functions appearing in Eqs. (13)(14), and subsequently in (12), are systematically generated when dealing with excited state wavefunctions of any given potential due to the zeros of Fgfunction. The effects of this consideration on the calculations are discussed in section 3. and considering Eq.…”

“…For instance, Refs. [6][7][8][9][10][11][12][13][14][15] involves some applications of the original idea discussed in [5].…”

A quantum pseudodot system with two-dimensional pseudoharmonic potential under external magnetic and AB flux fields

“…Recently, an alternative treatment is proposed for the calculations carried out within the frame of the NU method which removes a drawback in the original theory and bypasses some difficulties in solving the Schrödinger equation [44]. This formalism has also been extended to the relativistic wave equations [45].…”

“…The low-lying energy levels of two interacting electrons confined in a 2D parabolic quantum dot have been studied in magnetic field [45].…”