Quadratic and Coulomb Terms for the Spectrum of a Three-Electron Quantum Dot

摘要

We consider the Hamiltonian of a three-electron quantum dot composed of quadratic plus Coulomb terms and calculate the system's spectra. We next apply the hyperradius to reduce the three-body Schrodinger equation into a one-variable differential equation that is solvable. To avoid the complexity, the Taylor expansion of the effective potential is enters the problem and thereby a solution is found for the eigenvalues of the corresponding three-body Schrodinger equation in terms of the Wigner parameter.