A Unitary Transformation and Spectrum of a Three-Electron Quantum Dot

摘要

We consider the Hamiltonian of a three-electron quantum dot composed of parabolic confinement plus the Coulomb terms. Instead of using the Jacobi coordinates, we apply a unitary transformation to this system. To avoid the complexity, the Taylor expansion of the effective potential is introduced into the problem and thereby a solution is found for the eigenvalues of the corresponding three-body Schrodinger equation in terms of the Wigner parameter.