A Study on Radial Properties of Hydrogenic Ions using Laguerre Polynomials
Abstract
A preliminary study has been carried out on the radial properties of the hydrogenic systems using the Laguerre polynomial. The aims of this study were to investigate radial properties of hydrogenic ions by evaluating the radial probability density, the most probable radial distance and the average distance of electron from the nuclei of hydrogenic ions. Based on the research results for Z=1 to Z=10 with the principal quantum number (n)=1 to 5, 150 radial function forms, 150 radial probability density, 150 most probable radial distance values and 150 electron average distance values were obtained. The most probable radial distance from the nucleus was compared with the Bohr model and showed the same results as the Bohr model.
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References
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[3] A. Kartono, T. Winata and Sukirno, Applications of non-orthogonal Laguerre function basis in helium atom, Applied Mathematics and Computation, vol. 163, no.2, 2005, pp. 879-893.
[4] E. Boimau, R. K. Pingak and Bernandus, Penentuan energi keadaan dasar sistem atom helium muonik eksotis Heμμ menggunakan prinsip variasi, Jurnal Fisika: Fisika Sains dan Aplikasinya, vol. 2, no.1, 2017, pp:1-9.
[5] S. Purwaningsih, P. Nurwantoro and A. Hermanto, Calculation of ground state energy of helium using Hylleraas trial function expansion, International Journal of Engineering Research and Technology, vol.12, no.8, 2019, pp:1178-1182.
[6] R. K. Pingak, R. Kolmate and Bernandus, A simple matrix approach to determination of the helium atom energies, Jurnal Penelitian Fisika dan Aplikasinya, vol.9, no.1, 2019, pp. 10-21.
[7] S. Purwaningsih, Ground state energy of the helium using variational methods on trial wavefunctions, International Journal of Sciences: Basic and Applied Research, Vol. 54, No.4, 2020, pp:233-241.
[8] R. K. Pingak, A. Ahab, and U. A. Deta, Ground state energies of Helium-like ions using a simple parameter-free matrix method, Indonesian Journal of Chemistry, vol.21, no.4, pp.1003-1015.
[9] R. K. Pingak and A. Z. Johannes, Penentuan tingkat-tingkat energi vibrasi molekul hidrogen pada keadaan elektronik dasar menggunakan potensial Morse, Wahana Fisika, Vol. 5, No.1, 2020, pp:1-9.
[10] R. K. Pingak, A. Z. Johannes, F. Nitti and M. Z. Ndii, A theoretical study on vibrational energies of molecular hydrogen and its isotope using a semi-classical approximation, Indonesian Journal of Chemistry, Vol. 23, No.1, 2021, pp:725-739.
[11] Sutisna, Analytical solution of Schrodinger equation of the Harmonic oscillator system with position dependent mass using transformation method, Jurnal Ilmu Dasar, Vol. 10, No.2, 2009, pp: 114-120.
[12] P. Pandiangan, Solusi persamaan Schrodinger osilator harmonik dalam ruang momentum, Jurnal Matematika Sains dan Teknologi, Vol. 6, No. 1, 2005, pp:20-30.
[13] C. S. U. Luba, A. Warsito and R. K. Pingak, Kajian komputasi numerik energi elektron dalam sumur potensial berhingga, Jurnal Fisika: Fisika Sains dan Aplikasinya, Vol. 6, No.1, 2021, pp:17-23.
[14] P. Pandiangan, S. Adi and A. Arkundato, Metode elemen hingga untuk penyelesaian persamaan Schrodinger atom hidrogenik, Jurnal Matematika Sains dan Teknologi, Vol. 7, No. 1, 2006, pp:11-23
[15] F. Fuadah, S. H. B. Prastowo and L. Nuraini, Solusi persamaan Schrodinger atom deuterium dengan bilangan kuantum n=4, FKIP e-proceeding, Vol.3, No.2, 2019, pp:142-147.
[16] B. Supriadi, S. H. B. Prastowo, S. Bahri, Z. R. Ridlo and T. Prihandono, The stark effect on the wave function of tritium in relativistic condition, Journal of Physics: Conference Series, Vol. 997, No. 1, 2018, pp:012045.
[17] B. Supriadi, Z. R. Ridlo, F. Fuadah, M. A. Halim, M. Maulana and Y. R. Santoso, Solutions of spherical equation in 3 dimensions for hydrogen atom with quantum numbers 4
[19] B. Supriadi, A. Harijanto, M. Maulana, Z. R. Ridlo, W. D. Wisesa and A. Nurdiniaya, The function of the radial wave of a hydrogen atom in the principal quantum numbers (n) 4 and 5, Journal of Physics: Conference Series, Vol. 1211, no.1, 2019, 012052.
[20] R. K. Pingak, 2015, Bahan Ajar Fisika Kuantum, Kupang: Universitas Nusa Cendana.
[21] A. M. Juwono, 2017, Pendahuluan Fisika Kuantum. Malang: UB Press
[22] A. Kohnle, A. Jackson, and M. Paetkau, The difference between a probability and a probability density, The Physics Teacher, Vol. 57, 2019, pp. 190-192.
[23] R. A. Sani, and M. Kadri, 2017, Fisika kuantum. Jakarta: PT. Bumi Aksara.
[24] K. W. Ford, Niels Bohr’s first 1913 paper: still relevant, still exciting, still puzzling, The Physics Teacher, Vol. 56, 2018, pp. 500-502.
Published
2021-08-16
How to Cite
PANDU, Gerda et al.
A Study on Radial Properties of Hydrogenic Ions using Laguerre Polynomials.
BULETIN FISIKA, [S.l.], v. 23, n. 2, p. 78-84, aug. 2021.
ISSN 2580-9733.
Available at: <https://ojs.unud.ac.id/index.php/buletinfisika/article/view/76048>. Date accessed: 20 apr. 2024.
doi: https://doi.org/10.24843/BF.2022.v23.i02.p01.
Section
Articles
