Solutions to the Wheeler-Dewitt Equation Inspired by the String Effective Action

The Wheeler-DeWitt equation is derived from the bosonic sector of the heterotic string effective action assuming a toroidal compactification. The spatially closed, higher dimensional Friedmann-Robertson-Walker (FRW) cosmology is investigated and a suitable change of variables rewrites the equation in a canonical form. Real- and imaginary-phase exact solutions are found and a method of successive approximations is employed to find more general power series solutions. The quantum cosmology of the Bianchi IX universe is also investigated and a class of exact solutions is found.