Fibonacci numbers and electron orbitals

fractal-1239165__180The Fibonacci Sequence is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …
The next number is found by adding up the two numbers before it.

Fibonacci Sequence keeps appearing in mathematical expressions of nature, such as the number of flower petals.

chlorofluorocarbon-835796_960_720Could there be a quantum (or perhaps atomic) explanation, and indeed could this be a wellspring of other investigations? Let’s take a look at electron orbitals. My guess is that this is fertile ground.

So, orbitals describe where the electron is permitted. There are gaps. This was put forward by Einstein with regard to light, which he said came in discreet packets called quanta. Hence, quantum physics. Anyway, as with any spatial representation, there is a topology associated with that representation. In fact, topological insulators is a whole new area of study associated with this phenomena.

space time warpNow. let’s realize that these electrons have an electric charge. It’s a force. Like gravity. And so if you were to look at electron orbitals, where they are permitted to be, you will notice there are gaps. This fact begs for a topological analysis. And that is what I’ve done, at least on a cursory basis.

And here is where we get back to the Fibonacci Sequence. Because let’s look at these void areas. One can’t help but notice that the number of gaps increases with the energy level of the electron.

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In fact, there are null points between these orbitals, much like the Lagrange points that are related to objects in orbit around the planet Earth. And the number of Lagrange points, perhaps, coincides, in a toplogically relevant way, to the Fibonacci Sequence.

So, who’s up for the math?

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