Quasi-exact solutions for two interacting electrons in two-dimensional anisotropic dots

Abstract

We present an analysis of the two-dimensional Schrodinger equation for two electrons interacting via Coulombic force and confined in an anizotropic harmonic potential. The separable case of wy = 2wx is studied particularly carefully. The closed-form expressions for bound-state energies and the corresponding eigenfunctions are found at some particular values of wx. For highly-accurate determination of energy levels at other values of wx, we apply an efficient scheme based on the Frobenius expansion.

11 pages, 4 figures

References in corpus (3)

• Probing the Shape of Quantum Dots with Magnetic Fields
• Application of the Frobenius method to the Schrodinger equation for a spherically symmetric potential: anharmonic oscillator
• High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture

Cited by in corpus (5)

• Nonrelativistic molecular models under external magnetic and AB flux fields
• Effects of symmetry breaking in finite quantum systems
• Energy spectra and thermal properties of diatomic molecules in the presence of magnetic and AB fields with improved Kratzer potential
• Two-electron entanglement in elliptically deformed quantum dots
• Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies