Ok ok I made a relatively big blunder when sending the people from quantum mechanics using the Schödinger equation into the direction of the 3D complex numbers.
Because as a matter of fact, you cannot solve the factual Schrödinger equation in the 3D complex number system because there is no famous i to be found with the property that i^2 = -1.
You need a more advanced number system and I will explain that in detail in an upcoming post number three on the Schrödinger wave equation.
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In the meantime, it has not fallen on deaf ears on my side that after I posted the first Schrödinger post and I later did an internet search, suddenly with the search phrase ‘3Dcomplexnumbers’ I suddenly ended on number 1, 2 and 3.
So like expected it drew a lot of attention.
Therefore I would like to give a kind of present to the physical community because also not fallen on deaf ears, as far as I observe it physics people always try to use a product integral when they can.
Product integrals were my first serious mathematical invention, I found them while I was still trying to get my first year exam al the local university. Math professors almost never use product integrals because they are to stupid for that but physics people often put it in product integral representation.
How the history of that detail is I do not know, may be Paul Dirac had a bit to do with it…
Anyway, some time ago I wrote a pdf with the title
A tribute to Euler. Title: Ten styles for product integrals and product differentiation.
http://kinkytshirts.nl/pdfs/Product_integrals.pdf
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So far for the gift or the present, if you want to use other number systems beside the complex plane for depicting atomic orbitals or whatever you want to do with it, you also must know more about exponential circles and curves.
Physics people use so called ‘phase shift’ all of the time, but that is only multiplying some stuff with e to the power it or so. This is the sandpit exponential curve for toddlers.
In the world of the grown ups we have all kinds of other exponential circles and curves and guess what? I have a pdf for you with another 10 pieces of exponential circles & curves:
An overview of exponential circles and curves.
http://kinkytshirts.nl/pdfs/10_exponential_circles_and_curves.pdf
A possible way of parametrization of 3D exponential circles is given in the next picture and understanding this stuff is important when it comes to the third post related to the Schrödinger equation:
This is the end of this intro to the third Schrödinger post.
Have a nice life or try to get one.
Till updates.