We study one-dimensional reaction-diffusion models described by master
equations and their associated two-state quantum hamiltonians. By cho
osing appropriate rates, the equations of motion decouple into certain
subsets. We solve the first subset which has a close relation to the
problem of lattice electrons in an electric field. In this way we obta
in L(L - 1) + 1 energy levels of a quantum chain with L sites. The cor
responding hamiltonian depends on seven parameters and does not look i
ntegrable using conventional methods. As an application, we compute th
e dynamical critical exponent of a new type of kinetic Ising model.