Two-dimensional charged electron-hole complexes in magnetic fields: Keeping magnetic translations preserved

Eigenstates of 2D charged electron-hole complexes in magnetic fields are considered. The operator formalism that allows one to partially separate the center-of-mass motion from internal degrees of freedom is presented. The scheme using magnetic translations is developed for calculating in strong magnetic fields the eigenspectra of negatively charged excitons X^-, a bound state of two electrons and one hole.