Computational Modeling and Visualization of Quantum Wavefunctions in The Particle-in-a-Box and Hydrogen Atom

Aldwin Zalukhu; Shella Garelita; Alrizal; Jesi Pebralia; Dapfa Farrizo Altop; Fairuz Athaya Zahran Tane; Nada Oktaviani

doi:10.35895/rf.v6i2.84

Authors

Aldwin Zalukhu Department of Physics, Faculty of Science and Technology, University of Jambi Author
Shella Garelita Department of Physics, Faculty of Science and Technology, University of Jambi Author
Alrizal Department of Physics, Faculty of Science and Technology, University of Jambi Author
Jesi Pebralia Department of Physics, Faculty of Science and Technology, University of Jambi Author
Dapfa Farrizo Altop Department of Physics, Faculty of Science and Technology, University of Jambi Author
Fairuz Athaya Zahran Tane Department of Physics, Faculty of Science and Technology, University of Jambi Author
Nada Oktaviani Department of Physics, Faculty of Science and Technology, University of Jambi Author

DOI:

https://doi.org/10.35895/rf.v6i2.84

Keywords:

Quantum, Physics, computational, Quantum Mechanics, Computational Physics, Hidrogen Atom

Abstract

This study models and visualizes quantum wavefunctions in two fundamental systems-namely the one-dimensional particle-in-a-box and the hydrogen atom-using a computational Python-based approach. The Schrödinger equation is solved analytically to obtain the wavefunctions and probability distributions, which are subsequently visualized in both two and three dimensions. For the particle-in-a-box system, the results demonstrate clear energy quantization, increasing numbers of nodes, and waveform evolution that aligns with theoretical predictions. In the hydrogen atom system, the modeling incorporates the radial and angular components of the wavefunction, producing realistic orbital representations such as 1s, 2p, 3p, and 3d according to the chosen quantum numbers n, l, and m. The resulting visualizations clearly illustrate the relationship between quantum numbers, nodal structure, and electron probability distributions. Overall, the study shows that computational modeling effectively bridges mathematical solutions and physical interpretation, providing a powerful tool for enhancing conceptual understanding in quantum mechanics education.

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