It is predicted that resonance coupling between two discrete electron
energy levels corresponding to different size-quantization quantum num
bers and different Landau quantum numbers can occur in a quantum well
in a quantizing magnetic field. The resonance coupling is due to the i
nteraction of an electron with LO phonons and results in the formation
of polaron states of a new type. It is shown that for a certain value
of the magnetic field, which depends on the splitting of the electron
size-quantization levels, the absorption peak and the two-phonon reso
nance Raman scattering peak split into two components, the separation
between which is determined by the electron-phonon coupling constant.
The resonance coupling between size-quantization levels with the same
Landau quantum numbers is also studied. The splitting of the peaks in
this case is virtually independent of the magnetic field and can be ob
served in much weaker fields. The experimental observation of the effe
ct will make it possible to determine the relative position of the ele
ctronic levels and the electron-phonon coupling constant. (C) 1997 Ame
rican Institute of Physics.