Conflict and agreement in the exact solutions of Schrodinger equation in a two and restricted three-body systems

Abstract

Using the undetermined coefficients method, we obtained the exact solution of Schrodinger equation of a three-body system, H2+ ion, in a restricted form. We found that its ground state energy when the nuclear distance becomes zero can be the same as that of a He+ ion. However, its radial wavefunction is e-r while the corresponding wavefunction is e-2r for a He+ ion, where r is the electron-nucleus distance. We tentatively discussed clues leading to the interesting difference in a hope to find exact solutions of Schrodinger equation for systems of three or more bodies.