Variational methods in the quantum three-body problem with Coulomb interaction

The paper presents the calculation of non-relativistic ionization energy levels for the ground state of the helium atom and the muonic helium atom. The calculations are based on the variational method of “exponential” expansion. The convergence of the calculated energy levels is investigated depending on the number of basis functions N. This allows us to state that the obtained energy values have an accuracy 30 significant digits of the helium atom and 25 significant digits for the muonic helium atom.