Ground State Energy of the Helium Using Variational Methods on Trial Wave Functions


  • Sri Purwaningsih Lecturer at department of Mathematic and Natural Science education, Jambi University, Jambi, 36361, Indonesia


Helium, Variational Methods


Helium is a quantum system that has two electrons and one proton, the calculation of the ground state energy of helium has been done by variational method, the advantages of variational method is that it can be performed flexible selection of wave function. The objective of this study is to calculate the ground state energy of helium by using variational methods on the new wave function. From the research results obtained the ground state energy of helium equal to -77.333 eV. The result of this calculation is close to the experimental value.


. A. B. Suleiman , A. Usman , Ionization energy of Screened Helium by Variational quantum Monte carlo Method, International Journal Of Science and Nature, Vol. 4(2) , p. 311-315, 2013.

. Sulaiman, I.O.B. Ewa, Variational quantum monte carlo of the ground state energy of hydrogen molecul, BAJOPAS. 3.1, p. 112-117, 2010.

. R. Shankar, Principles of Quantum Mechanics, Second Editions, Yale University, New Haven Connecticut Springer, 1994.

. D. Part, Introduction to Quantum Theory, third Edition, McGraw-Hill, Inc 1992.

. D.J. Griffith, Introduction to Quantum Mechanic, Secon Edition, Person Prentice Hall, 1992.

. Esposito, Naddeo, Majorana Solutions to the Two Electron Problem, Found Phys, Springer, Vol.42, pp.1586-1608, 2012.

. A. Banerjee, C. Kamal, A. Chowdhury, Calculation of Ground and Excited State Energies of Confined Helium Atom, Physics Latters A 350 , pp. 121-125, 2006.

. J.J. Sakurai, Modern Quantum Mechanics Revised Edition, Addison Wesley Publishing Company, New York, England, Amsterdam, Sydney, Singapore, 1994.

. H. E.Montgomery, N. Aquino, A.F. Riveros, The Ground State energy of a Helium Atom Under Strong Confinement, Physics Latters A 374 , pp.2044-2047, 2010.

. A. S. Davydov, Quantum Mechanics, Second Edition, Pergamon Press, Oxford New York, Toronto, 1973.

. A. F. Riveros, N. Aquino, H. E. Montgomery, Spherically Compressed Helium Atom Described by Perturbative and Variational Methods, Physics Letters A ELSEVIER, 374, pp. 1246-1252, 2010.

. S. B.Doma, F.N. El Gamma, Application of the Variational Monte Carlo Method to the Two-Electron Atom, Journal Applied Mathematics and Information Science, An International Journal, 5(1), pp. 20-33, 2010.

. P.Atkins, R. Friedman, Molecular Quantum Mechanics, Fourth Edition, Oxford University Press, 2005.

. G.W.F. Drake, Z. C. Yan, Variational Eigenvalues for the S State of Helium, Chemical Physics Letters 229, p. 486-490, August 1994.

. J. S.Sims, S. A. Hagstrom, High Precision Hy-CI Variational Calculations for the Ground State of Neutral Helium and Helium-Like Ions, International Journal Quantum Chemistry, Vol 90, p.1600-1609, April 2002.

. C. Amovilli , N.H. March, L.A.Howand, A. Nagy, Exact Hamiltonian for an Analytic Correlated Ground State Wave Function for He-Like Ions, Physics Letters A, ELSEVIER, 372, pp. 4053-4056, Maret 2008.

. S .Bhattacharyya, A. Bhattacharyya, B. Taludar and N.C Deb, Analytical Approach to the Helium Atom Ground State using Correlated Wave Functions, J. Phys.B: At. Mol. Opt. Phys. 29, pp. L147-L150. 1996.

. S.E.Koonin, D.C.Meredith, Computational Physics Fortran Version, Addison Wesley Publishing Company, 1985.

. C. Schwartz, Ground State of the Helium Atom, Physical Review, Vol. 128, No.3, Nov 1962.

. E. Buendia, F.J. Galvez, P.Maldonado, A.Sarsa, Explicitly Correlated Wave Functions for Atoms and Single Charged Ions from Li through Sr: Variational and Diffusion Monte Carlo Results, Chemical Physics Letters, 615, p. 21-25, October 2014.




How to Cite

Purwaningsih, S. . (2020). Ground State Energy of the Helium Using Variational Methods on Trial Wave Functions. International Journal of Sciences: Basic and Applied Research (IJSBAR), 54(4), 233–241. Retrieved from