Abstract
We have extended the previous analysis of the quantum inverse problem for the Alfv\'en wave propogation by incorporating boundary conditions other than the periodic ones. Our approach is that of Sklyanin [Func. Ana. Appl. 21, 164 (1986)], which allows one to introduce different boundary conditions at the two ends. A generalized Bethe ansatz is used to deduce the eigenvalues of the Hamiltonian. An immediate outcome of our analysis is the effect of finite-size corrections, which is essential to study scale invariance and conformal properties of the model.
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