Scalar products of the state vectors in the totally asymmetric exactly solvable models on a ring

The exactly solvable totally asymmetric models of the low dimensional non-equilibrium physics on a ring, namely the totally asymmetric simple exclusion process and the totally asymmetric simple zero range process, are considered. The Quantum Inverse Method allows to calculate the scalar products of the state vectors of the models and to represent the answers in the determinantal form. It is shown that the eigenvectors of the models form a complete orthogonal basis. The projections of the state vectors on a stationary states, time independent ones, are studied.