Multiparameter optimization of optical nonlinearities in semiconductor quantum wells by supersymmetric quantum mechanics

Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schrödinger Hamiltonians

“…As to the possible physical applications of our obtained potentials in the position dependent mass background, let us mention that it will be interesting to use supersymmetric quantum mechanics to generate isospectral potentials that depend on a specified number of scalar parameters by multiple deletion and restoring of some levels of the original potential in the position dependent mass scenario so as to make them suitable for multiparameter optimization of optical nonlinearities in semiconductor quantum wells. This particular problem was dealt in ref [51], taking the constant effective mass m * .…”

Exact Solutions of Effective-Mass Schrödinger Equations

“…There is another interesting point behind the present results. A systematic procedure based on the inverse spectral theory and supersymmetric transformations has been recently proposed [24] for optimized design of semiconductor quantum well structures via tailoring the quantum well potential, which enables shifting bound states in a quantum well and makes the search for the best desired energy spectrum and potential shape. By varying the free parameters appearing in the procedure one can then design a convenient optimized structure.…”

“…There is another reason for the consideration of the work presented in this section. Among various potential shapes (quantum well profiles), there is one which has attracted some research attention recently: this is the case of Pöschl-Teller potential with a constant electron mass [23,24] . Unfortunately, this idealized potential is not realizable in the common, graded ternary alloy based quantum wells, because of the effective mass therein necessarily varies, together with the potential.…”