  We investigate the ground and excited states of interacting electrons in a
quantum point contact using exact diagonalization method. We find that strongly
localized states in the point contact appear when a new conductance channel
opens due to momentum mismatch. These localized states form magnetic impurity
states which are stable in a finite regime of chemical potential and excitation
energy. Interestingly, these magnetic impurities have ferromagnetic coupling,
which shed light on the experimentally observed puzzling coexistence of Kondo
correlation and spin filtering in a quantum point contact.
