Calculation of the energy spectrum of the quantum periodic three-particle Toda lattice

The quantum periodic three-particle Toda lattice is considered. For its Hamiltonian, the energy spectrum is calculated in terms of the orthogonal basis in Cartesian coordinates. The eigenstates are classified according to the irreducible representations of the C3v-point group. The spectral statistical properties are analyzed and shown to demonstrate a fairly good agreement with the theoretical predictions for the integrable system