The electronic structures of superlattices under an in-plane magnetic field are studied by the method of expansion with sine functions. The electronic and hole magnetic energy levels are obtained as functions of $k_x$,$k_y$ and the intensity of the magnetic field. The density of states and the magnetic-optical transition matrix elements are discussed. The variations of the binding energy of the heavy- and light-hole magnetic excitons with the magnetic field and the well width are also obtained. Finally, the electronic energy levels in the magnetic field along an arbitrary direction in the yz plane are calculated.

• Received 7 June 1989

DOI:https://doi.org/10.1103/PhysRevB.40.8508