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All Journal VALENSI Jurnal Ilmu Dasar POSITRON Jurnal Penelitian Fisika dan Aplikasinya (JPFA) BULETIN FISIKA Indonesian Journal of Chemistry Jurnal Fisika : Fisika Sains dan Aplikasinya Magnetic: Research Journal of Physics and It’s Application Jurnal Pengabdian Kepada Masyarakat (JPKM) Zadama: Jurnal Pengabdian Masyarakat Jurnal Pendidikan dan Pengabdian Masyarakat Molekul: Jurnal Ilmiah Kimia Jurna Beta Kimia Wahana Fisika : Jurnal Fisika dan Terapannya
Pingak, Redi Kristian
Universitas Nusa Cendana
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Journal : POSITRON

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Quantum Anharmonic Oscillators: A Truncated Matrix Approach Redi Kristian Pingak; Albert Zicko Johannes; Minsyahril Bukit; Zakarias Seba Ngara
POSITRON Vol 11, No 1 (2021): Vol. 11 No. 1 Edition
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam, Univetsitas Tanjungpura

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (477.967 KB) | DOI: 10.26418/positron.v11i1.44369

Abstract

This study aims at implementing a truncated matrix approach based on harmonic oscillator eigenfunctions to calculate energy eigenvalues of anharmonic oscillators containing quadratic, quartic, sextic, octic, and decic anharmonicities. The accuracy of the matrix method is also tested. Using this method, the wave functions of the anharmonic oscillators were written as a linear combination of some finite number of harmonic oscillator basis states. Results showed that calculation with 100 basis states generated accurate energies of oscillators with relatively small coupling constants, with computation time less than 1 minute. Including more basis states could result in more correct digits. For instance, using 300 harmonic oscillator basis states in a simple Mathematica code in about 8 minutes, highly accurate energies of the oscillators were obtained for relatively small coupling constants, with up to 15 correct digits. Reasonable accuracy was also found for much larger coupling constants with at least three correct digits for some low lying energies of the oscillators reported in this study. Some of our results contained more correct digits than other results reported in the literature.
Approximate Analytical Solution of the Ground State Problem of He and He-like Ions using Symmetrized-Hydrogenic States Pingak, Redi Kristian
POSITRON Vol 14, No 1 (2024): Vol. 14 No. 1 Edition
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam, Univetsitas Tanjungpura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26418/positron.v14i1.75417

Abstract

The matrix method using three symmetrized-hydrogenic basis states has been applied to analytically obtain an approximate solution to the Schrödinger equation of the Helium atom and some He-like ions (2Z10). This study aims at obtaining more accurate ground state energies of the systems compared to our previous calculation using un-symmetrized basis states and some other simple calculations in the literature. The contribution of the symmetrized basis states on the ground state energies of the systems is also investigated. The time-independent Schrödinger equation involving a 3×3 Hamiltonian matrix, formed by hydrogenic s-states, was analytically solved to obtain three energy eigenvalues of the systems as well as their corresponding eigenvectors. Results showed that the 1s2 energies of the systems were more accurate than our previous unsymmetrized basis calculations, with significant error reduction observed for He and Li+. With the same matrix size, the ground state energies of He and He-like ions obtained from three symmetrized basis states in this study were found to be closer to the exact and experimental energies than those obtained from unsymmetrized basis states. It was also demonstrated that the |100;100 state made the largest contribution to the ground state energies of the systems, i.e. about 90.9% for He and around 99.9% for Ne8+, and consequently the smallest contribution came from the other two symmetrized states (less than 1%). To conclude, the calculated ground state energies were more accurate than some other simple calculations reported in the literature.
Co-Authors Abdul Wahid Albert Z. Johannes Alexia Lemau Ali Warsito Amaral, Madalena A. Andreas Ch. Louk Andreas Christian Louk Andreas Christian Louk Anggi Arni Biha Atika Ahab Atika S. Ahab Bartholomeus Pasangka Bernandus Bernandus Bernandus Bernandus Bernandus Bernandus, Bernandus Bukit, Minsyahril Candra Satrio Umbu Luba Christine Mbiliyora Debi Lodo Ratu Elisabeth Boimau Eltra E. Barus Fidelis Nitti Gerda Pandu Godensius Tematur Hadi I Sutaji Hery L. Sianturi Intan M.P. Dewi Intan Riani Solo Jacob, Johanes Eliaser Johannes, Albert Z. Johannes, Albert Zicko Jonshon Tarigan Kapitan, Origenes Boy Kolmate, Rosara Kristantia Mida Subah Kristina Siu Lapailaka, Titus Larbi Setti Laura A. S. Lapono Leonardus Nengga Lerrick, Reinner Ishaq Luther Kadang Magdalena M. Y. Missa Mamut, Anastasia Maria Lurumutin Umrisu Maria S. Mali Marselinus E. Dandara Maunino, Mariani R. Meksianis Zadrak Ndii Minsyahril Bukit Minsyahril Bukit Minsyahril Bukit Minsyharil Bukit Modhe, Katarina Naat, Johnson N. Ndii, Meksianis Z Pasangka, Bartholomeus Refli, Refli Rensini, William Antoni Rosara Kolmate Roswita T. Saman Setiawan, Ely Severianus Wunda Sherlly Ledoh Soukaina Bouhmaidi Sriwiana Laalobang Sutaji, Hadi Imam Tanesib, Jehunias Leonidas Tarigan, Jhonson Tarigan, Jonshon Utama Alan Deta Yasinta Kresnawati Yovilia Medi Yuditha Ignasia Bete Zakarias Seba Ngara