44 questions linked to/from QM without complex numbers
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### Is it possible to formulate the Schrödinger equation in a manner that excludes imaginary numbers? [duplicate]

In the most general sense, the Time Dependent Schrödinger Equation (TDSE) reads $$\hat{H} \Psi = i \hbar ~{{\mathrm d} \over {\mathrm dt}}\Psi$$ Is it possible to get rid of the $i$ entirely? Does ...
1 vote
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### Are Imaginary Numbers Really “Imaginary?” [duplicate]

I find the naming convention of “Imaginary” misleading, as it does give a sense that the quantity is merely an abstract construct used to mitigate the difficulties of performing some mathematical ...
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### Can a complex wave function just be seen as two real functions describing a particle and antiparticle state? [duplicate]

Let's assume electromagnetism. There are two charges. The wave function is complex but can be seen canonically as a vector in $\mathbb{R}^2$. Can we see one of the components as the electron and the ...
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### Why is $i$ used in the equations for quantum mechanics? [duplicate]

Coming from someone who knows a tiny bit about the subject but who really wants to learn. I know it's the square root of -1 but I would like some insight as to why it's used at all.
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### Why is it necessary to use the imaginary number in QM? [duplicate]

My professor argues that one of the fundamentally unique properties of Quantum Mechanics is that the imaginary unit i is not removable (you can't avoid using it, unlike in other areas of physics like ...
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### Is there a way to explain quantum mechanics without invoking complex numbers? [duplicate]

"Every possible history starting from a particular state and ending at a particular state is assigned a complex number by some predefined rules in particular that the complex number is the product of ...
1 vote
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### Does Quantum Mechanics need imaginary numbers? [duplicate]

In quantum mechanics, we assume wavefunctions are complex valued, and that probability amplitudes are given by the modulus of the wavefunction squared. This formalism can correctly explain ...
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### Does it make a difference if we treat the wavefunction as having two real components instead of one real and one imaginary component? [duplicate]

I understand that the wavefunction in Quantum Mechanics is usually treated as a complex vector with one real and one imaginary component. Does it make an actual difference in terms of the answers we ...
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### Are complex numbers really needed in quantum mechanics? [duplicate]

I have been studying some Lie theory recently and I came across the idea of representing complex numbers using matrices, e.g. 1= \begin{pmatrix} 1 & 0\\ 0 & 1\\ \end{pmatrix} , i= \begin{...
1 vote
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### The Field $\mathbb{F}$ of A Hilbert Space [duplicate]

Is it always necessary for the field of some arbitrary Hilbert space I define to describe a system be a field of complex numbers only? Is it possible to have a field of naturals, or reals? Since the ...
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### Complex numbers in quantum mechanics [duplicate]

Are complex numbers used in the way the are in quantum mechanics for convenience sake? Or are they fundamental to quantum mechanics. In other words can quantum mechanics be completely described ...
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### What makes a theory "Quantum"?

Say you cook up a model about a physical system. Such a model consists of, say, a system of differential equations. What criterion decides whether the model is classical or quantum-mechanical? None ...
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### About the complex nature of the wave function?

1. Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
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### Discreteness and Determinism in Superstrings?

So Gerard 't Hooft has a brand new paper (thanks to Mitchell Porter for making me aware of it) so this is somewhat of a expansion to the question I posed on this site a month or so ago regarding 't ...