Expectation and Uncertainty of Helium Ion (He^+ ) Electron Position in the Position Space Wave Function at Quantum Numbers n ? 4
Abstract
The positive helium ion consists of two protons and one orbital electron to be viewed as a hydrogenic atom. The use of ions has very potential, especially in the development of spintronic devices and plasma-based sterilization. This study aims to determine the expected value and position uncertainty of He^+ ion electrons. Determination of the expected value and position uncertainty is done by analytical calculation through the Schrodinger method approach, especially the radial part at quantum number n?4, and numerical calculation with the help of a simulation program. The results showed that the main quantum number and orbital n, l influence the expectation value and position uncertainty. The greater the main quantum number n, the expectation value of electron position decreases and the uncertainty of electron position increases. At the same time, the increase in the orbital quantum number l has an impact on the value, which tends to go down. This research is in accordance with de Broglie's hypothesis about the nature of dualism and the principle of uncertainty in the review of position space.
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References
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[4] B. Supriadi, F. K. A. Anggraeni, N. Faridah, and E. M. Jannah, Fisika Kuantum. Jember: UPT Penerbitan Universitas Jember, 2022.
[5] R. Juge et al., “Helium Ions Put Magnetic Skyrmions on the Track,” Nano Lett. ACS Publ., vol. 21, no. 7, pp. 2989–2996, 2021.
[6] W. D. Saputro, A. R. Wibowo, A. Maulidiyah, and Y. Hendrawan, “Rancang Bangun Alat Sterilisasi Buah Manggis Berbasis Cold Atmospheric Plasma (CAP),” J. Ilm. Teknol. Pertan. Agrotechno, vol. 3, no. 2, p. 313, 2019, doi: 10.24843/jitpa.2018.v03.i02.p01.
[7] K. S. Krane, Modern Physics, 4th ed. Hoboken: John Wiley & Sons, Inc, 2020.
[8] N. Andelita, I. W. Sudiarta, and D. W. Kurniawidi, “Penerapan Algoritma Kuantum Variational Quantum Eigensolver (VQE) untuk Menentukan Energi Keadaan Dasar Dimer Helium,” J. Fis., vol. 11, no. 2, pp. 53–59, 2021, doi: 10.15294/jf.v11i2.30192.
[9] S. Sutopo, Pengantar Mekanika Kuantum: Transformasi Pemikiran dari Fisika Klasik ke Fisika Kuantum, 1st ed. Malang: Media Nusa Creative, 2023.
[10] F. Rusydi, Buku Ajar Fisika Kuantum Fungsi Gelombang, Energi Potensial, dan Operator. Surabaya: Airlangga University Press, 2022.
[11] Sunarmi, “Distribusi Probabilitas Radial Elektron Sistem Molekul Dalam Pengaruh Potensial Kratzer Dengan Metode Parametrik NikiForov-Uvarov,” J. Inov. Pendidik. dan Sains, vol. 4, no. 3, pp. 151–158, 2023.
[12] A. M. Juwono, Pendahuluan Fisika Kuantum, 1st ed. Malang: UB Press, 2017.
[13] D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed. Cambridge: Cambridge University Press, 2018.
[14] G. Pandu, R. K. Pingak, A. Z. Johannes, and Z. S. Ngara, “Kajian Sifat Radial Ion Hidrogenik Menggunakan Polinomial Laguerre,” Bul. Fis., vol. 23, no. 2, pp. 78–84, 2022.
[15] B. Supriadi, A. Z. L. Kinanti, E. E. Putri, A. R. Rosyidan, D. Natasha, and C. Sutantri, “Application Of Laguerre Polynomial Equation In Solving Schrodinger Equation Radial Section Of Helium Ion,” IOSR J. Appl. Phys., vol. 16, no. 1, pp. 22–31, 2024, doi: 10.9790/4861-1601012231.
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[17] N. Nuryono, Kimia Anorganik: Struktur dan Ikatan. Yogyakarta: Gajah Mada University Press, 2018.
[18] C. L. Arora, S. Chand’s Success Guide (Questions and Answers): Refresher Course in Physics Volume II (LPSPE). New Delhi: S. Chand Publishing, 2022.
[19] V. Sugiyono, Mekanika Kuantum, 1st ed. Yogyakarta: CAPS, 2023.
[20] L. Subagyo and A. Nuryadin, Pengantar Fisika Kuantum, 1st ed. Samarinda: Mulawarman University Press, 2018.
[21] A. Halim and F. Herliana, Pengantar Fisika Kuantum, 1st ed. Banda Aceh: Syiah Kuala University Press, 2020.
[22] B. H. Saputra, B. Supriadi, and S. H. B. Prastowo, “Ketidakpastian Momentum Atom Deuterium Menggunakan Pendekatan Ketidakpastian Heisenberg Pada Bilangan Kuantum n ≤ 3,” Semin. Nas. Pendidik. Fis. 2019, vol. 4, no. 1, pp. 57–64, 2019.
[23] R. A. Sani and M. Kadri, Fisika Kuantum, 1st ed. Jakarta: Bumi Aksara, 2017.
[24] A. R. Pratikha, B. Supriadi, and R. D. Handayani, “Electron’s Position Expectation Values and Energy Spectrum of Lithium Ion (Li^(2+)) on Principal Quantum Number n≤3,” J. Penelit. Pendidik. IPA, vol. 8, no. 1, pp. 252–256, 2022, doi: 10.29303/jppipa.v8i1.840.
[25] B. Supriadi and L. Nuraini, Fisika Atom: Teori & Aplikasinya. Jember: UPT Percetakan & Penerbitan Universitas Jember, 2019.
[26] B. Supriadi, H. Mardhiana, W. I. Kristiawan, D. Kamalia, and I. K. Sari, “Expected Value of Helium Ion Electron Momentum in Momentum Space with Primary Quantum Numbers n ≤ 3,” J. Penelit. Pendidik. IPA, vol. 9, no. 10, pp. 8467–8472, 2023, doi: 10.29303/jppipa.v9i10.3861.
[27] N. A. Ridha et al., Fisika Kuantum, 1st ed. Padang: CV. Gita Lentera, 2024.
[28] J. S. Dehesa and D. Puertas-Centeno, “Multidimensional hydrogenic states: position and momentum expectation values,” J. Phys. B At. Mol. Opt. Phys., vol. 54, no. 14pp, 2021.
Published
2025-05-22
How to Cite
AFIDAH, Zidan; SUPRIADI, Bambang; HANDAYANI, Rif'ati Dina.
Expectation and Uncertainty of Helium Ion (He^+ ) Electron Position in the Position Space Wave Function at Quantum Numbers n ? 4.
BULETIN FISIKA, [S.l.], v. 26, n. 1, p. 88 – 95, may 2025.
ISSN 2580-9733.
Available at: <http://103.29.196.112/index.php/buletinfisika/article/view/124497>. Date accessed: 16 dec. 2025.
doi: https://doi.org/10.24843/BF.2025.v26.i01.p11.
Section
Articles
