Analytical solution of the Schrödinger equation for the hydrogen molecular ion $H_2^{+}$

Abstract

The full analytical solution of the Schrödinger equation for the hydrogen molecular ion $H_2^{+}$ (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 $H_2^{+}$ at different internuclear separations.

4 pages, 1 figure. Corrected typos, changed a term, edited affiliation