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The beautiful Schrödinger equation calculates the waves that describe where an electron exists around an atom. It can only give the probability of locating the electron shown by the white shaded areas and this "opens the door" to the difficulty of interpreting quantum physics!
A different form of Schrödinger's equation can give the quantum energy levels of the electron.
The animation time steps through the simplest numerical calculation of the 2D Schrödinger equation.
The electron (described by a "wave packet" and seen as the white circular blob) is "released" initially having a vertical upwards momentum (given by the frequency of real & imaginary parts of the wave packet). Further info. including a page with code to plot a 2D wave function is here: sites.google.com/site/logiced...
The electron has a single negative unit of charge and is shown being attracted towards a single positive charge in the centre of the screen.
The wave function of the orbiting electron is shown evolving in time as a result of its electromagnetic attraction towards the nucleus, its own momentum and Heisenberg's uncertainty principle. The Schrödinger equation is sufficient to model all these phenomena.
The model plots ripples in the wave function that are a little like those filmed of a real electron by Mauritsson et al. shown in this KZfaq: • Scientists in Sweden f...
Ref. journals.aps.org/prl/abstract...