<Ciro Santilli>[Ciro]'s 10 cents: https://physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600

Why is there a <complex number> in the equation? Intuitively and mathematically:
* https://physics.stackexchange.com/questions/8062/about-the-complex-nature-of-the-wave-function
* https://physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600
* https://physics.stackexchange.com/questions/292947/is-it-possible-to-formulate-the-schr%C3%B6dinger-equation-in-a-manner-that-excludes-i

Some ideas:
* <explicit scalar form of the Maxwell's equations>

\Video[https://www.youtube.com/watch?v=f079K1f2WQk]
{title=Necessity of complex numbers in the <Schrödinger equation> by Barton Zwiebach (2017)}
{description=
This useless video doesn't really explain anything, he just says "it's needed because the equation has an $i$ in it".

The real explanation is: they are not needed, they just allow us to write the equation in a shorter form, which is always a win: https://physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600
}


Why are complex numbers used in the Schrodinger equation?