Abstract
The two state coupling problem in wave mechanics is solved in discretized form using the sign changes in the Sturm sequence of the Hamiltonian λ-determinant. The numerical algorithm is simple and fast; precision and accuracy can be separately controlled. The method is applied to the vibronic coupling problem in a diatomic (two closed channels) and the evolution of the adiabatic vibronic levels from the uncoupled (diabatic) states is demonstrated as a function of the strength of coupling. The method can be used for any symmetric pentadiagonal band matrix eigenvalue problem.
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