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We consider a system of two interacting particles with like but unequalcharges in a magnetic field in the planar geometry. We construct a completebasis of states compatible with both the axial symmetry and magnetictranslations. The basis is obtained using a canonical transformation thatgenerates effective quasiparticles with modified interactions. We establish aconnection of this transformation with the SU(2) algebra and make use of theSU(2) Baker-Campbell-Hausdorff formulas for evaluating the interaction matrixelements. We calculate analytically the eigenenergies of the problem (Haldanepseudopotentials) in the first few Landau levels for a relatively wide class ofinteraction potentials.

Interacting like charges in Landau levels: Planar geometry, symmetries, and effective quasiparticles