Indistinguishability and Counting: Teaching the role of different interpretations in Quantum Mechanics

The theme of indistinguishability in the context of Quantum Mechanics as opposed to a distinguishability in the context of Classical Mechanics has been treated for almost a century in terms of an essential difference between the way of counting in Quantum and Classical Mechanics. Such differences are based on the adoption of the principles of Heisenberg, Duality and Complementarity. In this work, we show that it is possible to avoid such considerations and derive the same results considering only the Correspondence Principle. This is done considering that, in the classic context, the quantum discrete energy levels become continuous or almost continuous. From these results, we indicate how to develop a discussion within the scope of teaching Quantum Mechanics that involves such principles and concepts and possible comparisons, working on ideas related to the interpretation of Quantum Mechanics with regard to this phenomenon, rarely developed in traditional courses.