Analytically exact solution of the Schrodinger equation for neutral helium in the ground state

• URL: http://arxiv.org/abs/2406.03020v3
• Date: Sat, 28 Sep 2024 19:06:46 GMT
• Title: Analytically exact solution of the Schrodinger equation for neutral helium in the ground state
• Authors: Frank Kowol,
• Abstract summary: This report presents the analytical solution of the Schrodinger equation and its corresponding wave function for the neutral helium or helium-like atoms in the ground state.
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• Abstract: This report presents the analytical solution of the Schrodinger equation and its corresponding wave function for the neutral helium or helium-like atoms in the ground state. The entangled state function of the electrons for S,L=0 is examined in detail. The basic idea is, though we treat the electron as a point like particle, not to understand its field as a point charge with the typical Coulomb field as in common approaches, but to solve the Schrodinger equation with an electric potential taking Heisenberg uncertainty principle into account. A method for describing a generic electron potential is derived, and the result was integrated into the Schrodinger equation. As a direct consequence the electromagnetic coupling of the electrons was investigated by introducing an effective interaction distance to describe vacuum polarization effects. The Schrodinger equation is solved using Laplace transformations. By determining the effective interaction distance iteratively, the ground state energy was calculated and compared with the literature values. It could be shown that with a given value the backward calculation of the effective interaction distance gives plausible results of the ground state energy thus providing us with a convincing method to describe the helium atom analytically. An upper limit estimation for the spatial dimension of the interaction distance for quantum-electrodynamical effects around the electron is given as well as the existence of a minimal distance of a stable bonding state between two electrons in the nucleonic field. As a result, the chemical inertness of helium regarding chemical reactions i.e., the principle of the "closed" electron shell - can be made plausible. The wave function found for the helium atom is compared with the known solutions for the hydrogen atom and Hylleraas function as well, and differences between those are worked out.

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