An alternative method for spectrum of a three-electron-quantum dot

We consider the Hamiltonian of a three-electron-quantum dot composed of parabolic confinement plus 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 Schrödinger equation in terms of the Wigner parameter.