On the Wheeler-De Witt equation in multidimensional cosmology with phenomenological matter

We consider the Wheller-De Witt equation for multidimensional cosmological models including phenomenological matter. In this way we find a generalized mechanical system in minisuperspace, which is integrable for a special mixture of tracefree matter components, generalizing the result of Ivashchuk, Melnikov, and Zhuk for the case of phenomenological matter. Just for a mixture of trace-free matter components, the dependence of the effective potential on the pseudotime in the corresponding minisuperspace may be separated. (author)