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A one-dimensional Schrödinger equation with the potential U(x) = (1 / 8R2)(x2 − R2)2 is considered. Asymptotic expansions for eigenvalues Eg,u = E0 ∓ 12ΔE for large R are presented. It is shown that the quantity ΔE obtained by means of the LCAO approximation exhibits incorrect behavior in the limit of large R. Comparisons of asymptotic formulae with results of numerical calculation are given.
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Damburg et al. (1971) studied this question.
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