Measuring the Density Matrix of Quantum-Modeled Cognitive States

Inspired by the principles of quantum mechanics, we constructed a model of students’ misconceptions about heat and temperature, conceptualized as a quantum system represented by a density matrix. Within this framework, the presence or absence of misconceptions is delineated as pure states, while the probability of mixed states is also considered, providing valuable insights into students’ cognition based on the mental models they employ when holding misconceptions. Using the analysis model previously employed by Lei Bao and Edward Redish, we represented these results in a density matrix. In our research, we utilized the Zeo and Zadnik Thermal Concept Evaluation among 282 students from a private university in Northeast Mexico. Our objective was to extract information from the analysis of multiple-choice questions designed to explore preconceptions, offering valuable educational insights beyond the typical Correct–Incorrect binary analysis of classical systems. Our findings reveal a probability of 0.72 for the appearance of misconceptions, 0.28 for their absence, and 0.43 for mixed states, while no significant disparities were observed based on gender or scholarship status, a notable difference was observed among programs (p < 0.05). These results are consistent with the previous literature, confirming a prevalence of misconceptions within the student population.