On the principles of elementary quantum mechanics

Abstract

Our problems are about α the correspondence a ↔ a between physicial quantities a and quantum operators a (quantization) and β the possibility of understanding the statistical character of quantum mechanics by averaging over uniquely determined processes as in classical statistical mechanics (interpretation). α and β are closely connected. Their meaning depends on the notion of observability. We have tried to put these problems in a form which is fit for discussion. We could not bring them to an issue. (We are inclined to restrict the meaning of α to the trivial correspondence a → a (for lim ħ → 0) and to deny the possibility suggested in β). Meanwhile special attention has been paid to the measuring process (coupling, entanglement; ignoration, infringement; selection, measurement). For the sake of simplicity the discussion has been confined to elementary non-relativistic quantum mechanics of scalar (spinless) systems with one linear degree of freedom without exchange. Exact mathematical rigour has not been aimed at.