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arXiv · 2502.21145

Hidden $sl(2)-$Symmetry of the Generalized Landau-Zener Vibronic Model

L. M. Nieto·S. Zarrinkamar
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Abstract

The one-dimensional harmonic vibronic model, which is a generalization of the so-called linear Landau-Zener model and appears in the form of coupled Schr\"{o}dinger equations, is revisited. After decoupling the components, the resulting fourth-order equation is shown to have a hidden $sl(2)$ algebra. The so-called exceptional part of the spectrum is then expressed in a rather simple way. For completeness, the eigenfunctions are obtained via the Bethe ansatz approach directly in position space.

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L. M. Nieto, S. Zarrinkamar. 2025-02-28. Hidden $sl(2)-$Symmetry of the Generalized Landau-Zener Vibronic Model. https://doi.org/10.1016/j.aop.2025.170126

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