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arXiv · 1103.4989

The H$_2^+$ molecular ion: a solution

Alexander V. Turbiner·Horacio Olivares-Pilón
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Abstract

Combining the WKB expansion at large distances and Perturbation Theory at small distances it is constructed a compact uniform approximation for eigenfunctions. For lowest states $1s\si_{g}$ and $2p\si_{u}$ this approximation provides the relative accuracy $\lesssim 10^{-5}$ (5 s.d.) for any real $x$ in eigenfunctions and for total energy $E(R)$ it gives 10-11 s.d. for internuclear distances $R \in [0,50]$. Corrections to proposed approximations are evaluated. Separation constants and the oscillator strength for the transition $1s\si_{g} \rar 2p\si_{u}$ are calculated and compared with existing data.

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Alexander V. Turbiner, Horacio Olivares-Pilón. 2011-03-25. The H$_2^+$ molecular ion: a solution. https://doi.org/10.1088/0953-4075/44/10/101002

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