  We extend the class of QM problems which permit for quasi-exact solutions.
Specifically, we consider planar motion of two interacting charges in a
constant uniform magnetic field. While Turbiner and Escobar-Ruiz (2013)
addressed the case of the Coulomb interaction between the particles, we explore
three other potentials. We do this by reducing the appropriate Hamiltonians to
the second-order polynomials in the generators of the representation of
$SL(2,C)$ group in the differential form. This allows us to perform partial
diagonalisation of the Hamiltonian, and to reduce the search for the first few
energies and the corresponding wave functions to an algebraic procedure.
