Functional Methods for the Solution of One-Dimensional Quantum Systems

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The book explores the Quantum Inverse Scattering Method applied to the XXX and XXZ spin chains with various boundary fields. It emphasizes the algebraic framework combining Yang-Baxter and Reflection algebras, addressing both diagonal and non-diagonal boundary conditions. While diagonal fields have been extensively studied through the algebraic Bethe ansatz, the author extends these findings to arbitrary chain lengths via non-linear integral equations. For non-diagonal fields, the separation of variables method is utilized, and a fusion hierarchy approach is introduced to derive non-linear integral equations for eigenvalue extraction.