Analytical Treatment of a Three-Electron-Quantum Dot Under Rashba Spin-Orbit Interaction

Bearing in mind the wide applications of quantum dots in modern technology, we theoretically investigate a three-electron-quantum dot in the presence of Rashba spin-orbit interaction by an analytical methodology. Using the Jacobi transformations as well as the hyperspherical coordinates; we separate the Hamiltonian in terms of center of mass and relative terms and thereby calculate the basic ingredients of such systems, i.e. the wavefunction and the energy spectra. We see that in some special cases, the solutions appear in the form of Bessel functions.