 Why are complex numbers used in the Schrodinger equation?

ID: why-are-complex-numbers-used-in-the-schrodinger-equation

Why is there a complex number in the equation? Intuitively and mathematically:

Some ideas:

Necessity of complex numbers in the Schrödinger equation by Barton Zwiebach (2017)

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: physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600

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