The jN method is applied within the context of a multigroup model to solve neutron transport problems for an infinite homogeneous slab with finite thickness under the assumption that the scattering of neutrons is spherically symmetric in the laboratory system. Stationary space-angle energy-dependent problems are treated as a special case of time-dependent problems. The numerical results for the vector flux generated by a stationary boundary source show that the j5 approximation gives an accuracy comparable to the S8 approximation in Carlson's theory, regardless of the size of the system. The transient time behavior of leakage neutrons is calculated on the basis of a one-group model and compared with Monte Carlo results. The j7 approximation gives values which agree well with those of the Monte Carlo calculation. In addition, the leakage neutron fluxes from copper blocks are obtained by the use of a 7 group j7 approximation as a function of time and the decay constants are compared with the experimentally observed values.