Bethe Ansatz for the Ruijsenaars Model of BC₁-Type
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math-phmath.MPnlin.SI
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ansatzbetheconstantscouplingmodelruijsenaarstypecase
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We consider one-dimensional elliptic Ruijsenaars model of type $BC_1$. It is given by a three-term difference Schr\"odinger operator $L$ containing 8 coupling constants. We show that when all coupling constants are integers, $L$ has meromorphic eigenfunctions expressed by a variant of Bethe ansatz. This result generalizes the Bethe ansatz formulas known in the $A_1$-case.
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