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The hydrogen atom

Geoffrey Brooker

Published Jul 16, 2021• 0 citations
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Abstract

Abstract The hydrogen atom is described by quantum mechanics. Radial wave functions are displayed, including those for large n (Rydberg atom). Emphasis is placed on the limits of classical motion, as giving a good indication of the atom's size. Positronium has the same size as hydrogen.
DOI
10.1093/oso/9780198857242.003.0013

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will be added. One can explain the nature of the term by examining the relativistic case. Below the formulas for the radial and angular parts of the wave function were evaluated. The term for the energetic levels of the hydrogen atom for specific quantum numbers was given. We calculated the values of several specific radial functions for different quantum numbers, as well as the values of the radial function at the origin of coordinates and wide apart. A number of mean values for different powers of r was calculated. For the continuous spectrum the radial eigenfunctions were calculated.
With an aim at the abstract conception of wave functions for hydrogen atom in quantum mechanics,this paper suggests the radial distribution,angular distribution and spatial distribution function of hydrogen atom electronic cloud,and also,Matlab software is used to plot their corresponding distribution charts.The analytical results indicate that the distribution patterns of hydrogen atom electronic clouds are co-determined by the radial and angular probability distribution,and that the electronic cloud distribution density is so uneven that the orbit trace can be observed.Accordingly,this method can reveal the radial,angular and spatial probability distribution laws of hydrogen atom electronic clouds intuitionally,whereby a new thinking way for analyzing the abstract wave function visualization in quantum mechanics is provided in this paper.