  We calculated some of the critical exponents of the directed percolation
universality class through exact numerical diagonalisations of the master
operator of the one-dimensional basic contact process. Perusal of the power
method together with finite-size scaling allowed us to achieve a high degree of
accuracy in our estimates with relatively little computational effort. A simple
reasoning leading to the appropriate choice of the microscopic time scale for
time-dependent simulations of Markov chains within the so called quantum chain
formulation is discussed. Our approach is applicable to any stochastic process
with a finite number of absorbing states.
