Resonant wavefunctions and exchange effect in nanostructures

It is shown that itinerant electrons in a nanostructure have the property, in a resonance energy range, that the wavefunctions exhibiting a resonance peak all have substantially the same position dependence within the 'quantum dot'. In the resonance energy range, they differ only by a Lorentzian function of energy including a phase factor. Consequently, for electron states with parallel spins there should be an exchange cancellation of their Coulomb interaction.