Tykhyy Y. Eigenstates of finite quantum integrable systems

In the thesis three particular cases of the quantum Baxter-Bazhanov-Stroganov chain are studied. The first is the generalized Ising model with periodic boundary condition, for this model the eigenstates of transfer-matrix and the matrix elements of the spin operator are computed. Also, another particular case is studied in the thesis - the ising-like Z_N-symmetric chain with fixed spins at the ends, for which the eigenvalues of its transfer-matrix are constructed. The third model studied in this thesis is a special particular case - relativistic Toda chain. The eigenstates for the chains with boundary interaction at one side and at both sides are constructed.