THE FORMAL REASONING OF QUANTUM MECHANICS: CAN WE MAKE IT CONCRETE? SHOULD WE?

The teaching and learning of quantum mechanics is very frequently postponed until relatively late in a student’s academic career. In U.S. universities students typically receive a quick introduction to some aspects of one-dimensional quantum mechanics from the end of the second or beginning of the third year of their university studies and then do not study quantum mechanics in any depth until the fourth year. Thus, the major concepts which have driven much of the development of physics and of modern technology during the 20th century are delayed until the end of a physicist’s academic career and are frequently not studied by other students at any time during their careers. One reason for this delay is the rather abstract nature of quantum mechanics itself. We can easily argue that, for the way in which quantum mechanics is traditionally taught, students need to have generally developed their formal reasoning skills. For example, formal operations, in the Piagetian sense, include hypothetical and deductive reasoning, abstract thought, use of symbolic representation, and the use of transformations. Quantum mechanics is a hypothetical system for understanding very small objects. It relies heavily on the use of symbolic representations and deduction to apply quantum mechanics to a variety of situations. Symmetry arguments, and therefore transformations, are a significant part of many presentations of quantum mechanics. Therefore overall, we can assume that the traditional mod