Answer by Ruben Verresen for QM without complex numbers
There is in fact a natural way to think of quantum mechanics without using complex numbers. This is closely related to the Hamiltonian-Jacobi (HJ) formulation of classical mechanics and gives an...
View ArticleAnswer by Ciro Santilli OurBigBook.com for QM without complex numbers
Explicit example of Schrodinger equation "without" complex numbersJust to give one completely explicit equation of the one particle case in position basis formulated only with real numbers (but two...
View ArticleAnswer by Lance for QM without complex numbers
Just to clarify, it sounds like you can.Today, complex numbers are still taught in universities and still advocated by some. They linger on in physics and engineering where sinusoidal waves or motion...
View ArticleAnswer by Gary Godfrey for QM without complex numbers
The rotation group, its representations, and their carrier spaces are fundamental parts of quantum mechanics. Every object in the universe is either a spin=0, 1/2, 1, 3/2, 2,… object. For the integer...
View ArticleAnswer by Moonraker for QM without complex numbers
Complex numbers are used for practical reasons only: QM includes helices and similar functions. The Euler formula$${e^{i\alpha}} = \sin \alpha + i \cos \alpha$$ is describing three-dimensional helices...
View ArticleAnswer by asmaier for QM without complex numbers
Let the old master Dirac speak:"One might think one could measure a complex dynamical variable by measuring separately its real and pure imaginary parts. But this would involve two measurements or two...
View ArticleAnswer by Christoph for QM without complex numbers
The nature of complex numbers in QM turned up in a recent discussion, and I got called a stupid hack for questioning their relevance. Mainly for therapeutic reasons, I wrote up my take on the issue:On...
View ArticleAnswer by akhmeteli for QM without complex numbers
Yes, we can have a theory of the same physics without complex numbers (without using pairs of real functions instead of complex functions), at least in some of the most important general quantum...
View ArticleAnswer by Terry Bollinger for QM without complex numbers
Frank, I would suggest buying or borrowing a copy of Richard Feynman's QED: The Strange Theory of Light and Matter. Or, you can just go directly to the online New Zealand video version of the lectures...
View ArticleAnswer by Ron Maimon for QM without complex numbers
The complex numbers in quantum mechanics are mostly a fake. They can be replaced everywhere by real numbers, but you need to have two wavefunctions to encode the real and imaginary parts. The reason is...
View ArticleAnswer by Steve Byrnes for QM without complex numbers
If you don't like complex numbers, you can use pairs of real numbers $(x,y)$. You can "add" two pairs by $(x,y)+(z,w) = (x+z,y+w)$, and you can "multiply" two pairs by $(x,y) * (z,w) = (xz-yw, xw+yz)$....
View ArticleAnswer by Christoph for QM without complex numbers
Update:This answer has been superseded by my second one. I'll leave it as-is for now as it is more concrete in some places. If a moderator thinks it should be deleted, feel free to do so.I do not know...
View ArticleAnswer by Alfred Centauri for QM without complex numbers
Complex numbers "show up" in many areas such as, for example, AC analysis in electrical engineering and Fourier analysis of real functions.The complex exponential, $e^{st},\ s = \sigma + i\omega$ shows...
View ArticleAnswer by dmckee --- ex-moderator kitten for QM without complex numbers
I am not very well versed in the history, but I believe that people doing classical wave physics had long since noted the close correspondence between the many $\sin \theta$s and $\cos \theta$s flying...
View ArticleQM without complex numbers
I am trying to understand how complex numbers made their way into QM. Can we have a theory of the same physics without complex numbers? If so, is the theory using complex numbers easier?
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