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We obtain analytic solution of the time-independent Schrodinger equation intwo dimensions for a charged particle moving in the field of an electricquadrupole. The solution is written as a series in terms of special functionsthat support a tridiagonal matrix representation for the angular and radialcomponents of the wave operator. This solution is for all energies, thediscrete (for bound states) as well as the continuous (for scattering states).The expansion coefficients of the wavefunction are written in terms oforthogonal polynomials satisfying three-term recursion relations. The chargedparticle could become bound to the quadrupole only if its moment exceeds acertain critical value.

Charged particle in the field an electric quadrupole in two dimensions