  We provide an algebraic procedure to find the eigenstates of two-charged
particles in an oscillator potential, known as {\it{Hooke's}} atom. For the
planar Hooke's atom, the exact eigenstates and single particle densities for
arbitrary azimuthal quantum number, are obtained analytically. Information
entropies associated with the wave functions for the relative motion are then
studied systematically, since the same incorporates the effect of the Coulomb
interaction. The {\it{quantum pottery}} of the information entropy density
reveals a number of intricate structures, which differ significantly for the
attractive and repulsive cases. We indicate the procedure to obtain the
approximate eigen states. Making use of the relationship of this dynamical
system with the quasi-exactly solvable systems, one can also develop a suitable
perturbation theory, involving the Coulomb coupling $Z$, for the approximate
wave functions.
