Linked Questions

10 votes
2 answers
2k 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 ...
Haru Fujimura's user avatar
1 vote
4 answers
421 views

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 ...
Joeseph123's user avatar
3 votes
2 answers
371 views

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 ...
NicAG's user avatar
  • 498
0 votes
2 answers
413 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.
Sam Cottle's user avatar
  • 1,542
2 votes
1 answer
1k views

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 ...
Marko Bakić's user avatar
0 votes
0 answers
282 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 ...
user avatar
1 vote
0 answers
119 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 ...
Jahan Claes's user avatar
  • 8,150
0 votes
1 answer
116 views

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 ...
Anders Gustafson's user avatar
3 votes
0 answers
106 views

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{...
Jieyan Zhu's user avatar
1 vote
0 answers
61 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 ...
Mahathi Vempati's user avatar
0 votes
0 answers
29 views

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 ...
Blue5000's user avatar
  • 303
167 votes
11 answers
17k 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 ...
AccidentalFourierTransform's user avatar
111 votes
15 answers
49k 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 ...
yayu's user avatar
  • 4,832
39 votes
11 answers
10k views

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 ...
QuestionAnswers's user avatar
60 votes
10 answers
9k views

Quantum made easy: so what *is* quantum mechanics all about? [closed]

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 ...
Jasmeru's user avatar
  • 1,138

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