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 Why are complex numbers used in the Schrodinger equation?

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

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Why are complex numbers used in the Schrodinger equation? by Ciro Santilli 37  Updated 2025-05-09  +Created 1970-01-01
Ciro's 10 cents: physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600
Why is there a complex number in the equation? Intuitively and mathematically:
  • physics.stackexchange.com/questions/8062/about-the-complex-nature-of-the-wave-function
  • physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600
  • 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 1.
Necessity of complex numbers in the Schrödinger equation by Barton Zwiebach (2017)
Source.
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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