Analytical solutions of the Schrodinger equation for the one-dimensional hydrogen molecular ion

TL;DR

This paper derives analytical solutions for the one-dimensional hydrogen molecular ion's Schrödinger equation, providing explicit formulas for its electronic energy states, which align with previous numerical findings.

Contribution

It offers the first closed-form analytical expressions for the energy curves of this system's ground and first excited states.

Findings

Analytical expressions match numerical solutions

Provides explicit formulas for energy states

Enhances understanding of molecular ion behavior

Abstract

We present analytical solutions of the Schrodinger equation for the one-dimensional hydrogen molecular ion. In particular, we present closed form expressions for the electronic energy curves of this system that correspond to the ground state and the first excited state. Our results agree with numerical solutions obtained before.