General form of the quantum-defect theory for-1/rα type of potentials with α > 2

We present a general formulation of the quantum-defect theory for systems with an attractive 1/r(alpha) type of asymptotic potentials with alpha > 2. Its structural differences from the standard theory for alpha <= 2, or from the semiclassical theory, is fully explained through a systematic understanding of quantum reflection above the threshold, and quantum connection formulas below the threshold.