Charged hydrogenic problem in a magnetic field: Noncommutative translations, unitary transformations, and coherent states

An operator formalism is developed for a description of charged electron-hole complexes in magnetic fields. A unitary transformation of the Hamiltonian that allows one to separate partially the center-of-mass and internal motions is proposed. We study an operator algebra that leads to the appearance of effective particles, electrons, and holes with modified interparticle interactions, and their coherent states in magnetic fields. The developed formalism is used for studying a two-dimensional negatively charged magnetoexciton X. It is shown that Fano resonances are present in the spectra of internal X transitions, indicating the existence of three-particle quasibound states embedded in the continuum of higher Landau levels.