  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 probabilities
P(x_1, ... ,x_N;t|y_1, ... ,y_N;0) of finding N particles on lattice sites x_1,
... ,x_N at time t with initial occupation y_1, ... ,y_N at time t=0.
