Remarks on Exact Solvability of Quantum Systems with Spatially Varying Effective Mass

Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable onedimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported in the literature and clarifies the relation between physically acceptable effective mass Hamiltonians.

Optical properties of Al_(x)Ga_(1-x)As/GaAs Woods-Saxon quantum well in the presence of hydrostatic pressure and applied electric field

The third harmonic generation(THG),linear and nonlinear optical absorption coefficients(OACs),and refractive index changes(RICs)are investigated in a Woods-Saxon quantum well(QW)modulated by the hydrostatic pressure and applied electric field.The effect of non-uniform aluminum doping(position-dependent effective mass(PDEM))on the mass of the system is discussed,and further to explore the influence of PDEM on the nonlinear THG,OACs,and RICs of the Woods-Saxon QW.These nonlinear optical properties above are obtained using the compact-density matrix formalism.The electron states in a Woods-Saxon QW under the constant effective mass(CEM)and PDEM are calculated by solving the Schr?dinger equation via the finite difference technique.The contributions from competing effects of the hydrostatic pressure and applied electric field to the nonlinear optical properties with CEM and PDEM are reported,as well as the comparison with each other.The observations reveal that the regulation of external fields and the influence of PDEM play an important role in the photoelectric properties of QW.