Understanding mathematical barriers to learning quantum mechanics and relativity: A qualitative study of Nigerian university students

Abstract

This qualitative study examined the mathematical barriers Nigerian undergraduate physics students encounter in learning quantum mechanics and relativity. It explored cognitive, pedagogical, and resource-related factors influencing students’ understanding of mathematically demanding concepts such as Hilbert spaces, linear operators, probabilistic formalism, Lorentz transformations, tensor calculus, and space-time curvature. Data were collected through semi-structured interviews and focus group discussions with 50 second- and third-year physics students from two Nigerian universities. Thematic analysis revealed persistent difficulties in understanding wave-particle duality, quantum superposition, the uncertainty principle, time dilation, and space-time curvature because these concepts conflict with classical intuition and rely on unfamiliar mathematical structures. Participants also identified lecture-dominated instruction, limited derivational engagement, overcrowded classrooms, and inadequate feedback as factors encouraging rote memorization rather than conceptual understanding. Inadequate access to interactive simulations, visual representations, modern textbooks, reliable internet, and laboratory facilities further hindered the development of mathematical intuition and coherent mental models. The findings indicate that learning challenges are shaped by both cognitive complexity and institutional constraints. The study recommends student-centred teaching, guided mathematical modelling, computational tools, interactive visualizations, smaller tutorial groups, and improved digital resources to strengthen mathematical reasoning, reduce misconceptions, and enhance modern physics learning in Nigerian universities and similar low-resource contexts.