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Hydrogen Atom Second Solution: Physical and Chemical Interpretations

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Abstract

We mainly study the ground state of the hydrogen atom in terms of the second kind of Legendre functions. We use a special self-adjoint transformation of the Schrödinger equation to obtain a self-adjoint operator and wave functions based on the second kind of Legendre functions without discontinuity. The projection of this wave function in terms of the complete set of the usual hydrogen atom solutions indicates the presence of a continuum. It is possible to infer that the normal hydrogen atom is weakly unstable in the presence of electromagnetic field, matter, or even quantum vacuum fluctuations due to the coupling with the continuum of the second solution. We discuss that the second solution behavior could be responsible for triggering the formation of chemical bonds. We also studied the temporal evolution of the second solution probability density, which shows an intricate structure.

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Acknowledgements

This study was supported by São Paulo Research Foundation (FAPESP, Fundação de Amparo a Pesquisa do Estado de São Paulo): grant 2019/12501-0 and partially financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES): Finance Code 001 and Fundación Carolina/Grupo de Tordesillas.

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Authors and Affiliations

  1. Chemistry Department, UFSCar, São Carlos, SP, 13565-905, Brazil

    Edgard Flauzino & Alejandro López-Castillo

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  1. Edgard Flauzino
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  2. Alejandro López-Castillo
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ALC wrote the main manuscript text; ALC and EF developed the studies.

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Correspondence to Alejandro López-Castillo.

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Flauzino, E., López-Castillo, A. Hydrogen Atom Second Solution: Physical and Chemical Interpretations. Int J Theor Phys 62, 80 (2023). https://doi.org/10.1007/s10773-023-05322-y

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