In order to support students in the development of expertise in quantum mechanics, we asked which concepts and structures can act as organizing principles of non-relativistic theory. The research question has been addressed in a multi-step process based on the analysis of categorization studies, on a content analysis of a sample of undergraduate textbooks, and on the results of existing research on learning difficulties. The answer consists of seven concept maps, intended as models of the organizing principles of quantum knowledge needed to account for the results of measurement and time evolution. By means of these instruments, it is possible to visualize and explore the different facets of the interplay between the vector structure of the quantum states and the operator structure of the observables, and to highlight the educational significance of the relations between observables. The maps can be used by instructors as a support for helping students build a well-organized knowledge structure and by researchers as a basis for the design of investigations into student understanding. While this framework may be adapted to different approaches and interpretive stances, it provides indications in favor of a spin-first approach over a waves-first one.

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