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All Journal Gravity : Jurnal Ilmiah Penelitian dan Pembelajaran Fisika
Kiki Dinda Octari
Universitas Jember
Astronomy Earth & Planetary Sciences Education Materials Science & Nanotechnology Physics

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The relationship between effective potential, radial probability distribution, and radial nodes in hydrogenic systems via a computational approach Bambang Supriadi; Dyah Arum Arimurti; Zilfiyatul Makida; Kiki Dinda Octari; Mah Citra Yunia Artika Putri; Ulvia Khoirunisa Bisanti; Nisrina Nafisah
Gravity : Jurnal Ilmiah Penelitian dan Pembelajaran Fisika Vol 12, No 2 (2026)
Publisher : Universitas Sultan Ageng Tirtayasa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62870/gravity.v12i2.40145

Abstract

The hydrogen atom is a fundamental system in quantum mechanics, yet studies that integrate the effective potential structure, radial probability distribution, and radial node patterns remain limited. This study aims to characterize the interrelationship of these three aspects through a computational approach. The method used is a combination of analytical solutions to the radial Schrödinger equation and numerical evaluation to calculate and visualize the effective potential, radial wave functions, and probability distributions. Furthermore, radial nodes are identified using a combination of the principal quantum number n and the azimuthal quantum number l. The results show that variations in l modify the topology of the effective potential through centrifugal resistance, while an increase in n broadens the probability distribution according to the scaling law . The radial node pattern follows the relation , indicating an interaction between radial excitation and angular momentum. Overall, the probability distribution and radial nodes are direct consequences of the effective potential structure. This study provides a unified analytical framework for comprehensively understanding the radial structure of hydrogenic systems.
Co-Authors Bambang Supriadi Dyah Arum Arimurti Mah Citra Yunia Artika Putri Nisrina Nafisah Ulvia Khoirunisa Bisanti Zilfiyatul Makida