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We discuss magnetoexcitons dispersion in single and coupled $GaAs-(Ga,Al)As$quantum wells using the Bethe-Salpeter (B-S) formalism. The B-S formalism inthe case of quantum wells provides an equation for the exciton wave functionwhich depends on two space variables plus the time variable, i.e. the B-Sequation is 2+1-dimensional equation. We compare the results formagnetoexcitons dispersion, obtained in the LLL approximations with the resultscalculated by solving the exact B-S equation. It is shown that the exact B-Sequation has an extra term (B-S term) that does not exist in the LLLapproximation. Within the framework of the variational method, we obtain that,(i) the ground-state energy of a heavy-hole magnetoexciton with a zero wavevector in $GaAs-(Ga,Al)As$ quantum wells, calculated by means of the exact B-Sequation, is very close to the ground-state energy, obtained in the LLLapproximation, (ii) in a strong perpendicular magnetic field the magnetoexcitondispersion (in-plane magnetoexciton mass) is determined mainly by the B-S termrather than the term that describes the electron-hole Coulomb interaction inthe LLL approximation.

Magnetoexciton dispersion in GaAs-(Ga,Al)As single and coupled quantum