Análise de uma possível transposição didática do paradoxo de Klein para o ensino médio

Abstract

The year 2025 marked the centenary of the proposition of the Schrödinger equations, which laid the foundations of quantum mechanics, which, despite being revolutionary, shows limitations at high energies where relativistic effects are indispensable. The initial response to this challenge came with the Klein-Gordon equation (1926-1927), the first attempt at a relativistic quantum theory. Its conceptual problems, such as negative probability density, motivated Dirac to develop his equation for spin-1/2 particles (1928), naturally introducing antiparticles and paving the way for Quantum Field Theory (QFT). This work aims to carry out a didactic transposition of the Klein paradox for high school education, through a bibliographical review of the most used physics textbooks in Brazil, grounded in David Ausubel’s theory of meaningful learning and Yves Chevallard’s theory of didactic transposition. Six textbook collections were analyzed, investigating the presence of modern and relativistic physics, the level of contextualization, and evidence of meaningful learning. The results indicate that modern physics is still treated in a peripheral and fragmented manner, with a predominance of traditional and rote learning approaches. Based on this analysis, a didactic proposal was developed, conceptually accessible for high school, using analogies, concept maps, simulations, and technological contextualizations, such as graphene and quantum tunneling, to introduce the Klein paradox qualitatively and meaningfully, respecting students’ subsumers and the guidelines of the Brazilian National Common Curricular Base (BNCC).