Two-dimensional space-charge layer in a tilted magnetic field

Combined intersubband cyclotron resonances in a quasi-two-dimensional space-charge layer with a magnetic field tilted with respect to the surface are studied through a simple single-electron model. Two alternative basis sets have been pointed out which enable one to obtain analytical matrix elements of the Hamiltonian for all values of the magnitude and the angle of tilt of the magnetic field. The effect of the coupling between electronic motions normal and parallel to the layer has been investigated in detail and is found to give rise to deviations in the expected values of the Landau spacings as functions of the tilt angle of the $B$ field. Optical spectra for such systems show some features in qualitative agreement with experiments and other calculations. The system is a prototype of nonseparable problems in two dimensions.