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

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 Schrödinger 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.

10 pages

References in corpus (5)

• Simulated Quantum Computation of Molecular Energies
• Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets
• Vibronic interactions in trilobite and butterfly Rydberg molecules
• Hidden $sl(2)$-algebraic structure in Rabi model and its 2-photon and two-mode generalizations
• Quantum-inspired classical algorithm for molecular vibronic spectra