Parton-hadron duality in QCD sum rules: Quantum-mechanical examples

Motivated by recent work on three-point QCD sum rules in heavy quark physics, we use simple quantum mechanical models to study the basic issue of duality in three-point sum rules. We show that while in all of these models the duality in two-point sum rules works fine, the duality in three-point sum rules may be 100% violated, leading to completely unreliable predictions for the matrix elements in question. The implications for three-point QCD sum rules are discussed. A new estimate for the parameter λ₁ of HQET is given.