The Radial Electron Density in the Hydrogen Atom and the Model of Oscillations in a Chain System

The radial electron distribution in the Hydrogen atom was analyzed for the ground state and low-lying excited states by means of a fractal scaling model originally published by Muller in this journal. It is shown that Muller’s standard model is not fully adequate to fit these data and an additional phase shift must be introduced into its mathematical apparatus. With this extension, the radial expectation values could be expressed on the logarithmic number line by very short continued fractions where all numerators are Euler’s number. Within the rounding accuracy, no numerical differences between the expectation values (calculated from the wavefunctions)and the corresponding modeled values exist, so the model matches these quantum mechanical data exactly. Besides that, Muller’s concept of states can be transferred to electron resonances and the radial expectation values can be interpreted as both, proton resonance lengths and electron resonance lengths. The analyzed data point to the fact that Muller’s model of oscillations in a chain system is compatible with quantum mechanics.