Summary
Our problems are about
α the correspondence a ←→ a between physical 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.
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Groenewold, H.J. (1946). On the Principles of Elementary Quantum Mechanics. In: On the Principles of Elementary Quantum Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-6065-2_1
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