Calculation of the diamagnetic shift in resonant-tunneling double-barrier $\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures

By using an iteration matrix formalism we calculate the transmission coefficient of $\frac{\mathrm{GaAs}}{{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}}$ double-barrier heterostructures under crossed magnetic and electric fields. A dispersion relation for the total energy of the electron is proposed from which the diamagnetic shift is derived. We extend our calculations to compare with experimental results in a single quantum well [N. J. Pulsford, J. Singleton, R. J. Nicholas, and C. T. B. Foxon, J. Phys. (Paris) Colloq. 48 C5-231 1987. This method can also be used to compute the transport properties in resonant tunneling devices under a strong magnetic field.