Transpositive Phenomena at the Interface Between Mathematics and Physics: The Case of Quantum Mechanics

Mathematics as a service course for other disciplines is a vivid issue in mathematics education. Yet, existing studies mainly focus on mathematics as being used, whereas in advanced physics their status is rather on an equal footing with the domain of application. In this article, we focus on the case of quantum mechanics. By presenting praxeological organisations from an introductory quantum mechanics course at the University of Montpellier (France) we wish to describe the linkage between mathematics and physics it shows, with a focus on linear algebra and Hilbert spaces. Our main concern is to investigate the transpositive phenomena that may occur when mathematics and physics are as intimately intertwined as is the case for quantum mechanics.