A method is described for the optimized design of quantum-well (QW) structu
res, in respect to maximizing the stimulated gain in optically pumped inter
subband lasers. It relies on applying supersymmetric quantum mechanics (SUS
YQM) to an initial Hamiltonian, In order to both map one bound state below
the spectral range of the initial Hamiltonian, and to generate a parameter-
controlled family of isospectral Hamiltonians with the desired energy spect
rum. By varying the control parameter, one changes the potential shape and,
thus, the values of dipole matrix elements and electron-phonon scattering
matrix elements. The use of this procedure is demonstrated by designing smo
othly graded and stepwise-constant A(1-x)Ga(1-x)As ternary alloy QWs, with
the self-consistent potential taken into account. Finally, the possibility
of employing layer interdiffusion to get optimal smooth potentials is discu
ssed.