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  • Paken Pandiangan
    Universitas Terbuka
  • Supriyadi Supriyadi
    Universitas Jember
  • A Arkundato
    Universitas Jember

Abstract


The research computed the energy levels and radial wave functions of the  Hydrogen Atom. The method used for computation was FEM (finite element method). Using the variational method approach, FEM was applied to the action integral of  Schrödinger equation. This lead to the eigenvalue equation in the form of  global matrix equation. The results of computation were depended on boundary of the action integral of Schrödinger equation and number of elements. For boundary 0 - 100a0 and 100 elements,  they were the realistic and best choice of computation to the closed  analytic results. The computation of first five energy levels resulted E1 = -0.99917211 R, E2 = -0.24984445 R, E3 = -0.11105532 R,           E4 = -0.06247405 R and  E5 = -0.03998598 R where 1 R= 13.6 eV. They had relative error under 0.1% to the analytic results.



 

Keywords

FEM, Hydrogen atom, Schrödinger equation.

References

Brasden, B. H. & Joachain, C. J. (1995). Physics of atoms and molecules. New York: John Wiley & Sons, Inc.

Brugioni, J. P. (1995). Finite element method in quantum mechanics. http://www.science.gmu.edu/~jbrugion/RTF/qm1.htm. Diambil 19 Oktober 2004.

Gasiorowicz, S. (1995). Quantum physics. USA: John Wiley & Sons, Inc.

Mohan, L. R. (2002). Finite element and boundary element applications in quantum mechanics. New York: Oxford University Press.

Nikishkov, G. P. (2004). Introduction to the finite elemen method. Lecture Note. University of Aizau, Japan.

Thankappan, V. K. (1985). Quantum mechanics. New Delhi: Wiley Eastern Limited.

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Published Aug 15, 2006
How to Cite
PANDIANGAN, Paken; SUPRIYADI, Supriyadi; ARKUNDATO, A. METODE ELEMEN HINGGA UNTUK PENYELESAIAN PERSAMAAN SCHRÖDINGER ATOM HIDROGENIK. Jurnal Matematika, Sains, Dan Teknologi, [S.l.], v. 7, n. 1, p. 11-23, aug. 2006. ISSN 2442-9147. Available at: <http://jurnal.ut.ac.id/index.php/JMST/article/view/511>. Date accessed: 23 nov. 2017.
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