Quantum model of Thomson helium atom

In the framework of the stationary perturbation theory, a quantum model of Thomson helium atom is considered. It is shown that from a formal mathematical point of view this problem is similar to the problem of two-electron states in a parabolic quantum dot. The estimation of the ground state energy of a quantum Thomson helium atom on the basis of Heisenberg's uncertainty principle is provided. Ground-state energy obtained in the oscillator basis and in the first order of perturbation theory and qualitative estimation give, respectively, upper and lower bounds of eigenvalues obtained in the framework of finite element method by numerical solution of the problem for the quantum model. The conditions of realization of Kohn theorem in such a system are discussed, when the values of the resonance frequencies are independent of the Coulomb interaction between electrons