Exact solution of the master equation for the asymmetric exclusion process

Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilitiesP(x₁,...,x_N;t/y ₁,...,y_N; 0) of findingN particles on lattices sitesx ₁,...,x_N at timet with initial occupationy ₁,...,y_N at timet=0.