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Different propositions of the uncertainty principle for position and momentum: integrating mathematical formalism, phenomenology and interpretations in the teaching of quantum theory

The Uncertainty Principle, proposed by the physicist Werner Heisenberg in 1927, is central to the development of Quantum Theory and since its summary assumes a plurality of interpretations, mathematical derivations and mental experiments that seek to explore it in depth. However, textbooks, which play an important role in the training of scientists and science teachers, usually choose to privilege only some of their main aspects and end up limiting the presentation of the Uncertainty Principle in Quantum Theory courses in higher education. In order to increase discussions about the Uncertainty Principle for the variables position and moment and contribute to the Quantum Theory Teaching, throughout this text we present the Uncertainty Principle at three different levels (mathematical formalism, phenomenology and interpretation). We started by rescuing, in a didactic way, four different historical derivations of the Uncertainty Principle: the Heisenberg and Weyl derivations for the variables position and momentum, and the Robertson and Schrodinger derivations for two observables any A and B. Then, we retake two thought experiments proposed by Heisenberg: the gamma-ray microscope and the electron passing through a slit. Finally, we present the four main schools of interpretation of the Uncertainty Principle.

Keywords
Uncertainty Principle; Quantum Theory; Physics Teaching


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