Abstract

It has been recognized that use of the effective mass theory for abrupt interfaces between different materials suffers from ambiguity in kinetic- energy operator ordering, caused by nonvanishing commutator of the momentum operator and the position-dependent effective mass. This leads to nonuniqueness of the Hamiltonian, which in its general form can be written as a one-parameter family of operators.¹ The matching conditions for the envelope wave function and its derivative at the interfaces are also parametrized.¹ Recently, Fu and Chao reported² that experimentally observable interband transition energies are not sensitive to the effective- mass operator ordering. In this paper, we demonstrate that optical transition energies do vary substantially with ordering. Specifically, we have analyzed GaAs/AlGaAs quantum wells using the transfer matrix technique.² We have investigated the effects of quantum well parameters, such as subband index, thicknesses of both constituent materials, and barrier height (composition) on the shifts of subband-edge energy, between the two extreme cases of operator ordering. Calculated energy levels are more sensitive to ordering for higher subbands and for decreasing well thickness. Increasing the barrier height or thickness in coupled quantum wells will also result in a larger shift of subband-edge energies. Comparison with available data allows us to choose the ordering that provides the best fit to experiment.

© 1991 Optical Society of America