We present a systematic study of excitonic and impurity states in semiconducting quantum wells within a fractional-dimensional space approach, in which the Schro¨dinger equation is solved in a noninteger-dimensional space where the interactions are assumed to occur in an isotropic effective environment. In this scheme, the fundamental quantity is the parameterDwhich defines the fractional dimension associated to the effective medium, and to the degree of anisotropy of the interactions. A direct procedure for determining the fractional dimensionality of the isotropic effective space is proposed in which one may obtain a reliable solution for the energies of the actual physical system under consideration. Explicit calculations of the fractional-dimensionalDparameter are made in the case of excitons and impurities in infinite-barrier quantum wells, with exciton and impurity binding energies found in excellent agreement with previous variational results. Calculations are also performed for exciton binding energies in finite-barrier quantum wells with good agreement with recent experimental results. ©1997 American Institute of Physics.