Analytical solution of the Schr\"odinger equation for the hydrogen molecular ion H2+
Abstract
The full analytical solution of the Schr\"odinger equation for the hydrogen molecular ion H2+ (special case of the quantum tree-body problem with the Coulomb interaction) is obtained first. The solution shows that the total wave function is a two-term function in the sense that it is a linear combination of the two linear independent wave functions. The two-term character of the total wave function was visualized in calculations of the total electron density of H2+ at different internuclear separations.
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