The article consists of two parts describing two associated properties of two-dimensional magnetoexcitons. In the first part, the theory of combined excitoncyclotron resonance in the quantum well structures is developed for a strong magnetic field. In the first part, we calculate the absorption band structure for optical quantum transitions with circularly polarized radiation creating a two-dimensional exciton and simultaneously exciting one of the resident electrons from the lowest to the first excited Landau level. In the second part, we discuss the collective elementary excitations of the system of two-dimensional magnetoexcitons in the ground state of Bose–Einstein condensation on the arbitrary wave vector k

0 in the Hartree–Fock approximation. The breaking of the gauge symmetry of the initial Hamiltonian was introduced following the idea proposed by Bogoliubov in his theory of quasi-averages. The energy spectrum of the collective elementary excitations is characterized by the interconnection of the exciton and plasmon branches.
International Journal of Quantum Chemistry, Vol 110, 177–194 (2010)