From wavefunctions to orbitals: a Mathematics–Physics–Chemistry model for quantum instruction

Source abstract

Abstract Quantum physics is a foundational topic in the education of natural sciences, science teacher education, and engineering, but it is also one of the subjects that causes substantial conceptual difficulties for students. An important reason is that learners must simultaneously use three different knowledge languages: the mathematical language of wavefunctions and operators, the physical language of states and measurement, and the chemical language of orbitals, electronic structure, and spectra. When these three disciplinary languages and the representations used within them are taught separately, students may manipulate formulas without understanding their physical meaning, or they may describe orbitals in chemistry while still identifying them with the classical trajectory of an electron. This study proposes and evaluates an interdisciplinary Mathematics–Physics–Chemistry instructional model for undergraduate quantum physics, focusing on three core concepts: the wavefunction, quantum probability, and the orbital. The model is grounded in theories of representational translation, conceptual change, and interdisciplinary STEM education. The research design uses a mixed-methods quasi-experimental approach, with 150 students divided into an experimental group and a control group, together with 10 instructors who participated in the validation of the instruments and the instructional model. The results show that the experimental group achieved greater improvement in conceptual understanding and reported higher perceived interdisciplinary representational translation competence, including perceived ability to connect Mathematics, Physics, and Chemistry. Because intact classes were used, these findings are interpreted as intervention-associated differences rather than as fully isolated causal effects. Misconception-linked responses concerning ‘the orbital is a trajectory’, ‘ | ψ | 2 is the real shape of the electron’, and ‘wavefunction normalization is only an algebraic procedure’ decreased more markedly in the experimental group than in the control group after the intervention. The paper contributes an instructional framework that can be used in the education of science teacher candidates, natural science students, and engineering students, while also suggesting a direction for empirical research on quantum education through an interdisciplinary approach.