Abstract

The essential role of classical mechanics in the “old quantum theory” is well known. With the rise of a genuine quantum formalism, classical analogies remained a powerful heuristic tool. However, classical insights soon proved problematic, and in some cases, even counterproductive. The case of the implementation of quantum canonical transformations provides a distinguished case study for the historian studying the circumstances which led to the transformation theory of London, Dirac and Jordan. The attempts to use canonical transformations in strict analogy to classical practice met serious difficulties as soon as one tried to accommodate the action-angle scheme. At some point, the very consistency of quantization went addressed because of the unclear quantum equivalence of classically equivalent Hamiltonians. The early attempts, often beset with ill-defined problems, are illustrative of the lack of understanding of the underlying mathematical scheme. The latter had to be properly appraised before the problem of the meaning of changing variables in quantum theory could be solved. This is why the latter proved instrumental in the discovery of transformation theory. Some of the problems which arose then are still highly instructive from the foundational point of view, and worth to be rediscovered, beyond their historical interest.