<![CDATA[Understanding high-dimensional spaces, particularly the fourth dimension, remains a major conceptual challenge in quantum physics education due to their abstract mathematical nature and the limitations of conventional visualization approaches. Although four-dimensional quantum systems have been extensively explored in theoretical and experimental physics, their pedagogical visualization remains limited and rarely integrated with computational modeling for instructional purposes. This study aims to develop and systematically evaluate a computational visualization framework for a four-dimensional particle in a box quantum system by: (1) constructing a numerical model using Python-based simulation, (2) implementing explicit dimension-reduction techniques to project 4D probability distributions into 3D and 2D representations, and (3) analyzing the structural and probabilistic features preserved in these projections. The results show that the projected visualizations preserve key signatures of the fourth dimension, demonstrated by a ground-state energy relative error of 0.14% and normalization accuracy of 99.98%, indicating high computational reliability. The resulting heatmaps and tesseract-based geometric representations provide interpretable visual structures that support spatial reasoning in quantum learning contexts. The novelty of this study lies in the explicit integration of high-dimensional quantum modeling, systematic dimension-reduction, and data-driven visualization within a single pedagogical framework, which transforms abstract four-dimensional quantum formalisms into accessible instructional representations. This study contributes a computationally grounded instructional model that supports the development of quantum literacy and conceptual understanding in modern physics education.]]>
Copyrights © 2026
