The energy spectrum of an electron in a semicondutor with a superlattice in a transverse magnetic field

A solution is obtained to the problem of the spectrum of an electron in a semiconductor with a one-dimensional superlattice in a magnetic field of arbitrary intensity that is transverse to the direction of periodicity. The change in the energy spectrum of the electron with a change in the magnetic field is traced. When the magnetic field is weak, the effective Hamiltonian method is valid; with strong fields, where the effect of the field on the state of the electron in the individual layers making up the superlattice is significant, it is found that the effective Hamiltonian method cannot be used.