Abstract
In this study the most simple approximation to the numerical solution for a Helium atom system is computed, dividing the problem in two independent Hydrogen systems and neglecting the inter-electronic term. The radial and spherical harmonic functions yield certain tendencies, relating the evolution of the quantum numbers and the shape of the probability density functions (PDF), that correspond to each combinations of n, l and m. The radial and angular PDF components return the already known result: there exist more probability to find the electron in its more stable level of energy, close to the nucleus. Also, it was computed the numerical/analytic solution for a Hamiltonian in which the inter-electronic term was replaced with a constant C in order to find a condition relating the energies and the inter-electronic distance.
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Notes
- 1.
We verify all these results with the use of the NDSolve routine from Mathematica with all its default values. For a future larger version of the code we expect to run our Mathematica script into a supercomputer.
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Acknowledgement
Special thanks to the National Institute of Supercomputing of Ecuador for allow us to perform the simulations in the Quinde I supercomputer, located at Innópolis, Urcuquí, Ecuador.
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Ramírez-Velásquez, J.M., Sanchez, J.A. (2019). Three Body Problem Applied to the Helium Atom System: The Independent Electron Approximation (IEA). In: Torres, M., Klapp, J. (eds) Supercomputing. ISUM 2019. Communications in Computer and Information Science, vol 1151. Springer, Cham. https://doi.org/10.1007/978-3-030-38043-4_8
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DOI: https://doi.org/10.1007/978-3-030-38043-4_8
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