30 questions linked to/from QM without complex numbers
571 views

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 ...
196 views

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 ...
95 views

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 ...
79 views

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 ...
54 views

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 ...
36 views

Can we discuss about quantum mechanical ideas without using complex numbers? [duplicate]

I used to believe firmly that the essence of quantum mechanics is complex number. Complex number makes the calculation of probability in quantum theory very different from that in classical ...
14k views

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 ...
29k views

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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Being a physics grad student, I got used to the weird concepts behind quantum mechanics (used to doesn't mean I fully understand it though). What I mean is that I'm not surprised anymore by the fact ...
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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 ...
4k views

Why are Only Real Things Measurable?

Why can't we measure imaginary numbers? I mean, we can take the projection of a complex wave to be the "viewable" part, so why are imaginary numbers given this immeasurable descriptor? Namely with ...
3k views

Can one do the maths of physics without using $\sqrt{-1}$?

The use of imaginary and complex values comes up in many physics and engineering derivations. I have a question about that: Is the use of complex numbers simply to make the process of derivation ...
We know $\Psi(x,t)$ is complex, but can $\Psi(x)$ be complex? I have seen particle in a box, well and harmonic oscillator. All have real solutions for time-independent Schrödinger equation. Hence, I ...