Parameter Perturbation Method for Helium Ground State Energy Calculation

Authors

  • Zhentao Luo

DOI:

https://doi.org/10.54097/hset.v64i.11277

Keywords:

Helium atom; Ground-state energy; Perturbation method; Harmonic oscillator.

Abstract

The ground-state energy is one of the most important pieces of information for research in various fields such as spectroscopy. However, the exact calculation of the value turns out to be challenging, and some approximation methods are needed. This paper is mainly focused on one of the approximations, the parameter perturbation method, and tries to investigate how well the method works to the helium ground-state energy calculation by comparing the approximated results with the experimental result and finding the relationship between the accuracy of the approximation and the orders of perturbation. Other commonly used approximation methods such as perturbation theory and variational principle are also introduced for comparisons and discussions. The paper finds that the parameter perturbation method turns out to be a desirable approach to approximate the helium ground-state energy because the approximated result is relatively easy to calculate and will get extremely close to the experimental result only within a few orders of perturbation. Therefore, the parameter perturbation method could become one of the potential candidates that researchers can use to estimate the energy levels for helium.

Downloads

Download data is not yet available.

References

Sakurai J. J., Napolitano J. Modern Quantum Mechanics Second Edition. Pearson Education, Inc., 89-92, 2011.

Courteille, P. W. Quantum Mechanics Applied to Atoms and Light. University of São Paulo, 2023, 216: 139-142.

University of Texas. Helium Atom. April 8, 2013. Retrieved on March 14, 2023. Retrieved from: https://farside.ph.utexas.edu/teaching/qm/lectures/node97.html

University of Virginia. Variational Methods. February 28, 2007. Retrieved on March 14, 2023. Retrieved from: http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/Variational_Methods.htm

Zhang C., Ning S., Lu Q. Research on the Ground State Energy of Helium-like Atom by Parameter Perturbation Method. College Physics, 2015, 34(2): 32-32.

Zhang C. Research on Ground State Energy of Helium-like Ion C4+ by Using Parameter Perturbation Method. Journal of Guangdong University of Petrochemical Technology, 2018, 28(6): 70-72.

Zhang C., Xi W., Lu J., Li T. Highly Accurate Ground State Energy Calculation of Helium-like Ion N5+ and O6+ Based on the Parameter Perturbation Method. Journal of Sichuan University, 2016, 53(5): 1062-1066.

Wu F., Meng L. Ground State Energy of Beryllium Atom with Parameter Perturbation Method. Chin. Phys. B, 2018, 27: 093101.

Wu F., Huang B., Meng L. Solving Eigenvalues of Nonlinear Harmonic Oscillators by Parameter Perturbation Method. College Physics, 2018, 37(5): 35-38.

National Institute of Standards and Technology. NIST Atomic Spectra Database Ionization Energies Form. September 28, 2012. Retrieved on March 14, 2023. Retrieved from: https://physics.nist.gov/PhysRefData/ASD/ionEnergy.html.

Dalgarno A., Stewart A. L. A Perturbation Calculation of Properties of the Helium Iso-electronic Sequence. Physical Sciences, 1958, 247(1249): 250.

Downloads

Published

21-08-2023