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

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

2011-03-25

arxiv.org/abs/1103.4989v2

Physics

Quantum Physics

16 pages, 4 figures, 6 tables, typos are corrected and small additions are inserted, to be published at JPB (fast track comm)

Scientific paper

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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