COMPUTATIONAL VISUALIZATION OF HYPOTHETICAL FOUR-DIMENSIONAL QUANTUM SYSTEMS FOR PEDAGOGICAL PURPOSES
DOI:
https://doi.org/10.59052/edufisika.v11i2.49885Keywords:
Computational visualization, Four-dimensional quantum systems, Physics education, Quantum simulationAbstract
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.
References
A, S., Sarjan, M., Rokhmat, J., Arizona, K., Sucilestari, R., Syahidi, K., Syamsuddin, S., & Mertha, I. G. (2022). Kebermaknaan Fisika Kuantum Sebagai Solusi Membangun Karakter Peserta Didik. Jurnal Ilmiah Profesi Pendidikan, 7(2b), 672–679. https://doi.org/10.29303/jipp.v7i2b.555
Abbas Shah, S. F., Mazhar, T., Shahzad, T., khan, M. A., Ghadi, Y. Y., & Hamam, H. (2024). Integrating educational theories with virtual reality: Enhancing engineering education and VR laboratories. In Social Sciences and Humanities Open (Vol. 10). Elsevier Ltd. https://doi.org/10.1016/j.ssaho.2024.101207
Abeltino, A., Serantoni, C., De Giulio, M. M., Riente, A., Capezzone, S., Esposito, R., Spirito, M. De, & Maulucci, G. (2026). Quantum Metabolic Avatar: A digital replica of metabolism enhanced by quantum algorithms. Expert Systems with Applications, 296. https://doi.org/10.1016/j.eswa.2025.129045
Acevedo, P., Magana, A. J., Walsh, Y., Will, H., Benes, B., & Mousas, C. (2024). Embodied immersive virtual reality to enhance the conceptual understanding of charged particles: A qualitative study. Computers and Education: X Reality, 5. https://doi.org/10.1016/j.cexr.2024.100075
Aharonov, D. (1998). arXiv:quant-ph/9812037v1 15 Dec 1998. In World Scien-tific.
Akhsan, H., Ramadhona, T., Lestari, M., Oktavia, D. R., & Hafitri, R. (2025). Implementasi Fomalisme: Prinsip Ketidakpastian Heisenberg dan Notasi Dirac dalam Teknologi Modern. In Jurnal Teori dan Aplikasi Fisika (Vol. 13, Issue 02).
Araújo, R. E., Ximenes, R., & Dias, E. O. (2024). Space-time-symmetric extension of quantum mechanics: Interpretation and arrival-time predictions. Physical Review A, 109(1). https://doi.org/10.1103/PhysRevA.109.012221
Argüello-Luengo, J., Bhattacharya, U., Celi, A., Chhajlany, R. W., Grass, T., Płodzień, M., Rakshit, D., Salamon, T., Stornati, P., Tarruell, L., & Lewenstein, M. (2024). Synthetic dimensions for topological and quantum phases. Communications Physics, 7(1). https://doi.org/10.1038/s42005-024-01636-3
Banda, H. J., & Nzabahimana, J. (2021). Effect of integrating physics education technology simulations on students’ conceptual understanding in physics: A review of literature. Physical Review Physics Education Research, 17(2). https://doi.org/10.1103/PhysRevPhysEducRes.17.023108
Blay, K. B., Darko, A., Hwang, S., Brilakis, I., Foster, F., & Wei, R. (2025). Ensuring information security resilience in Digital-enabled Construction Projects (DCP) through quantum security technologies. In Automation in Construction (Vol. 179). Elsevier B.V. https://doi.org/10.1016/j.autcon.2025.106480
Bley, J., Rexigel, E., Arias, A., Krupp, L., Steinert, S., Longen, N., Lukowicz, P., Küchemann, S., Kuhn, J., Kiefer-Emmanouilidis, M., & Widera, A. (2025). Visualizing Quantum States: A Pilot Study on Problem Solving in Quantum Information Science Education. https://doi.org/10.1103/hdpv-frft
Bouhiron, J.-B. (n.d.). Realisation of an atomic quantum Hall system in four dimensions. https://theses.hal.science/tel-04816923v1
Cajori, F. (1926). Origins of Fourth Dimension Concepts. In Source: The American Mathematical Monthly (Vol. 33, Issue 8).
Chang, K. C., Cheng, X., Sarihan, M. C., & Wong, C. W. (2025). Recent advances in high-dimensional quantum frequency combs. In Newton (Vol. 1, Issue 1). Cell Press. https://doi.org/10.1016/j.newton.2025.100024
Dias, E. O. (2025). Space-time-symmetric non-relativistic quantum mechanics: Time and position of arrival and an extension of a Wheeler-DeWitt-type equation. http://arxiv.org/abs/2308.04376
Dodevska, M., Zdravevski, E., Chorbev, I., Kostoska, M., Branco, F., Coelho, P. J., Pires, I. M., & Lameski, P. (2025). Virtual reality as a learning tool: Evaluating the use and effectiveness of simulation laboratories in educational settings. In Social Sciences and Humanities Open (Vol. 12). Elsevier Ltd. https://doi.org/10.1016/j.ssaho.2025.101742
Flegr, S., Kuhn, J., & Scheiter, K. (2023). When the whole is greater than the sum of its parts: Combining real and virtual experiments in science education. Computers and Education, 197. https://doi.org/10.1016/j.compedu.2023.104745
Fu, B., Yang, L., Yuan, Y., Yang, J., Li, H., Fan, Z., Yan, S., Lu, G., Zhang, D., Gong, Q., & Xu, X. (2025). Robust strong coupling of single quantum emitters with plasmonic nanocavity on one-dimensional photonic crystal substrate. Fundamental Research. https://doi.org/10.1016/j.fmre.2025.04.012
Galvão, L. Q., Rosa, S. E. da, & Cruz, C. (2024). Possibilities and Challenges of Introducing Quantum Computing in High School Education. Revista Brasileira de Ensino de Fisica, 46. https://doi.org/10.1590/1806-9126-RBEF-2024-0213
Gambrell, J., & Brewe, E. (2024). Analyzing interviews on computational thinking for introductory physics students: Toward a generalized assessment. Physical Review Physics Education Research, 20(1). https://doi.org/10.1103/PhysRevPhysEducRes.20.010128
Guo, D., Hu, T., & Hong, J. (2025). Localization and dynamics in one-dimensional and two-dimensional Gaussian disordered quantum spin systems. Results in Physics, 76. https://doi.org/10.1016/j.rinp.2025.108407
Hari Rajan, M., Herbert, C., & Polly, P. (2025). A synthetic review of learning theories, elements and virtual environment simulation types to improve learning within higher education. Thinking Skills and Creativity, 56. https://doi.org/10.1016/j.tsc.2024.101732
Hu, Z., Shukla, K., Karniadakis, G. E., & Kawaguchi, K. (2024). Tackling the curse of dimensionality with physics-informed neural networks. Neural Networks, 176. https://doi.org/10.1016/j.neunet.2024.106369
Irvani, A. I., Rochintaniawati, D., Riandi, R., Sinaga, P., & Henukh, A. (2024). Analysis of Quantum Physics Lectures from the Perspective of the MBKM and OBE Based Higher Education Curriculum. Jurnal Pendidikan Fisika Dan Teknologi, 10(1), 44–54. https://doi.org/10.29303/jpft.v10i1.6390
Küchemann, S., Ubben, M., Dzsotjan, D., Mukhametov, S., Weidner, C. A., Qerimi, L., Kuhn, J., Heusler, S., & Sherson, J. F. (2023). The impact of an interactive visualization and simulation tool on learning quantum physics: Results of an eye-tracking study. http://arxiv.org/abs/2302.06286
Luis A. Herrera, Rosa M. Rodríguez, & Carlos R. Lopez. (2024). The Role Of Digital Simulation in Enhancing Conceptual Understanding Of Physics Among University Students. International Journal of Mathematics and Science Education, 1(1), 62–68. https://doi.org/10.62951/ijmse.v1i1.82
Ma, W., Liang, D., Qian, Q., Mo, Q., Zhao, S., Cai, W., Chen, J., & Zang, Z. (2023). Near-unity quantum yield in zero-dimensional lead-free manganese-based halides for flexible X-ray imaging with high spatial resolution. EScience, 3(2). https://doi.org/10.1016/j.esci.2022.100089
Nita, L., Mazzoli Smith, L., Chancellor, N., & Cramman, H. (2023). The challenge and opportunities of quantum literacy for future education and transdisciplinary problem-solving. Research in Science and Technological Education, 41(2), 564–580. https://doi.org/10.1080/02635143.2021.1920905
Radu, I., Huang, X., Kestin, G., & Schneider, B. (2023). How augmented reality influences student learning and inquiry styles: A study of 1-1 physics remote AR tutoring. Computers and Education: X Reality, 2. https://doi.org/10.1016/j.cexr.2023.100011
Rahayu, M. S. I., & Kuswanto, H. (2020). Development of android-based comics integrated with scientific approach in physics learning. Journal of Physics: Conference Series, 1440(1). https://doi.org/10.1088/1742-6596/1440/1/012040
ReinderssDuit HanssE Fischer Editors, D. (n.d.). Models and Modeling in Science Education Multiple Representations in Physics Education. http://www.springer.com/series/6931
Rexigel, E., Qerimi, L., Bley, J., Malone, S., Küchemann, S., & Kuhn, J. (2025). Learning quantum properties with informationally redundant external representations: An eye-tracking study. http://arxiv.org/abs/2501.07389
Riskawati, R., Rusdiana, D., & B, H. (2024). Quantum Physics Lecture Profile in Supporting Student Computation Thinking (CT) Integration Program. Gravity : Jurnal Ilmiah Penelitian Dan Pembelajaran Fisika, 10(1). https://doi.org/10.30870/gravity.v8i2.23343
Sakai, E. (2005). On the principles of quantum mechanics.
Seegerer, S., & Nakahara, M. (2024). Bridging the Quantum Gap: Addressing Challenges in Training Individuals in Quantum Computing Using Self-Guided Learning Resources. The Journal of Computational Science Education, 15(1), 13–14. https://doi.org/10.22369/issn.2153-4136/15/1/3
Sephton, B., Vallés, A., Nape, I., Cox, M. A., Steinlechner, F., Konrad, T., Torres, J. P., Roux, F. S., & Forbes, A. (2023). Quantum transport of high-dimensional spatial information with a nonlinear detector. Nature Communications, 14(1). https://doi.org/10.1038/s41467-023-43949-x
Sheng, L., Zhang, X., Mu, Q., Li, H., & Ren, J. (2025). Novel carbon molecular sieve membranes for CO2 separation derived from the zero-dimension carbon quantum dots doped polyimide. Journal of Membrane Science Letters, 5(2). https://doi.org/10.1016/j.memlet.2025.100105
Shi, B. Sen, & Zhou, Z. Y. (2021). Quantum interface for high-dimensional quantum states encoded in an orbital angular momentum space. In Fundamental Research (Vol. 1, Issue 1, pp. 88–90). KeAi Communications Co. https://doi.org/10.1016/j.fmre.2021.01.001
Shofiyah, N., Jatmiko, B., Suprapto, N., Prahani, B. K., & Anggraeni, D. M. (2025). The use of technology to scientific reasoning in science education: A bibliometric and content analysis of research papers. In Social Sciences and Humanities Open (Vol. 11). Elsevier Ltd. https://doi.org/10.1016/j.ssaho.2025.101534
Song, G., Wang, X., & Ghannam, R. (2024). Immersive quantum: A systematic literature review of XR in quantum technology education. In Computers and Education: X Reality (Vol. 5). Elsevier B.V. https://doi.org/10.1016/j.cexr.2024.100087
Tarng, W., & Pei, M. C. (2023). Application of Virtual Reality in Learning Quantum Mechanics. Applied Sciences (Switzerland), 13(19). https://doi.org/10.3390/app131910618
Tóth, K., & Bitzenbauer, P. (2025). A teaching approach to quantum computing at the secondary school level. Eurasia Journal of Mathematics, Science and Technology Education, 21(11). https://doi.org/10.29333/ejmste/17388
Truskewycz, A., Beker, S., Ball, A. S., & Cole, I. (2019). Photoluminescence measurements of carbon quantum dots within three-dimensional hydrogel matrices using a high throughput 96 well plate method. MethodsX, 6, 437–441. https://doi.org/10.1016/j.mex.2019.02.014
Ullah, A. M. M. S. (2020). Concept map and knowledge. In Education Sciences (Vol. 10, Issue 9, pp. 1–2). MDPI AG. https://doi.org/10.3390/educsci10090246
Wójcik, D., Białynicki-Birula, I., & Życzkowski, K. (2000). Time evolution of quantum fractals. Physical Review Letters, 85(24), 5022–5025. https://doi.org/https://doi.org/10.1103/PhysRevLett.85.5022
Wu, W., Castronovo, F., Luo, Y., Liang, A., Gomez, F., Kassis, S., & Wolcott, A. (2025). Faculty learning community (FLC) as a structured intervention to prepare higher education STEM faculty for classroom integration of extended reality (XR). Computers and Education: X Reality, 6. https://doi.org/10.1016/j.cexr.2025.100096
Yakkou, H., Chillali, A., Elyamani, N. E. E. kadri, & El khattabi, K. (2024). The effect of using simulator “evolution of electrical systems’’ in electricity lessons on students’ motivation and academic performance. Heliyon, 10(15). https://doi.org/10.1016/j.heliyon.2024.e34770
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Afrizal, Arinda, Ami, Hamdi Akhsan, Melly
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
![](<a href="https://doaj.org/toc/2477-7935" target="_blank" style="display: block; width: 150px; height: auto;"><img src="https://doaj.org/static/doaj/images/logo/seal.png"/></a>){kind=logo}
