We investigate theoretically the optical and electrical properties of parabolic semiconducting quantum well structures. In our calculations, we assume that the confinement of the carriers is in an infinite parabolic well. We show that the carrier mobility in the plane perpendicular to the direction of confinements is directly proportional to the harmonic oscillator length k whose value depends upon the partitioning of the band gap discontinuity between the conduction and valence bands. We have also calculated the linewidth for intra-subband resonances which should occur for electromagnetic radiation polarized in the direction of carrier confinement and show that the linewidth is inversely proportional to k and directly proportional to the temperature when the linewidth is dominated by acoustic phonon scattering. The absorption coefficient for interband optical transitions shows equally spaced steps as a function of photon energy where the value of the spacing between adjacent steps depends upon the partitioning of the band gap discontinuity. Carrier freeze-out in the intrinsic conduction occurs due to the presence of zero point energies in the conduction and valence bands arising from the carrier confinement. These zero point energies also are found to depend upon the partitioning of the band gap discontinuities. Therefore, information about the partitioning of the energy band gap discontinuity between the conduction and valence bands can be obtained by measuring these various optical and electrical transport properties of a parabolic quantum well semiconducting structure under those conditions when the model of an infinite parabolic well approximates the real system.