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An Equation Similar to the Schroedinger Equation for the Atom with an Electron, Which Moves, from the Point of View of an Observer

Edigles Guedes

Published Mar 1, 2013• 0 citations
OpenAlex

Abstract

When we conduct a thought experiment, in which the observer moves and can see the model for Schroedinger wave equation of atom with one electron, we create a wave function and calculate its wave eigenfunction acceptable, in spherical coordinates.

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The trajectory of motion of a scattering electron in the Coulomb potential from the wave function of the Schroedinger equation is presented in two ways, spherical polar coordinates and Temple coordinates, and is compared with each other and with the corresponding motion of classical mechanics. A good correspondence among dynamics by wave functions and the classical dynamics has been acknowledged by comparing computed examples.Detailed computing examples discriminate the optimal dynamics of the wave function that should be verified by an experiment.
In the first of five parts in a series, the Schroedinger equation is solved in spherical polar coordinates to yield wave functions that enable an accurate calculation of the frequencies and intensities of lines in the absorption spectrum of the Lyman series in the vacuum-ultraviolet region. Accurate plots of surfaces of amplitude functions illustrate the variation of shapes and sizes varying with quantum numbers k, l, m for comparison with the corresponding plots of amplitude functions in other systems of coordinates.
We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for |x|>a and by an arbitrary function for |x|<a, using elementary methods. The study of this problem sheds light on usual errors made in discussions of the asymptotic behavior of the eigenfunctions of the quantum harmonic oscillator and can also be used for the analysis of the eigenfunctions of the hydrogen atom. We present explicit results for the energy levels of a potential of this class, used to model the confinement of electrons in nanostructures.