Linked Questions

20
votes
10answers
6k views

Physical interpretation of complex numbers [duplicate]

Complex numbers are used widely in quantum mechanics and the waveform, is there a physical interpretation of what this means about the structure of the universe? Why is it not used in macro physics? ...
5
votes
2answers
1k views

In classical mechanics, are complex numbers unphysical? [duplicate]

Possible Duplicate: Physics math without $\sqrt{-1}$ When I produce a complex final solution to a problem that began without complex coefficients at all, I have so far (with my limited expertise) ...
1
vote
4answers
165 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 ...
4
votes
1answer
719 views

Complex variables in classical mechanics [duplicate]

In quantum mechanics complex numbers are absolutely essential because of the relation $$[\hat q_i,\hat p_j]=i\hbar\delta_{ij}.$$ But is complex number also essential anywhere in the formalism of ...
2
votes
2answers
405 views

Dimensional aspects of the imaginary unit $i$ in physics [duplicate]

From a real world perspective each dimension in the 3-D Cartesian System can be represented by an axis that is perpendicular to 2 other axes. I read somewhere else that the effect of ${i}$ is to ...
1
vote
1answer
140 views

Complex theory in physics [duplicate]

I'm a physics graduate and usually encounter with complex numbers in physics. For example, in electrical engineering, Why do we express capacitive reactance as an imaginary number..? Can't it be ...
0
votes
0answers
37 views

Can we get rid of complex number? [duplicate]

Complex number is very weird to me, especially so when they appear in engineering and physics equations. It is possible to represent complex number as real matrix where $i = \begin{pmatrix} 0&1\\...
79
votes
14answers
30k 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 ...
81
votes
12answers
20k views

QM 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?
34
votes
7answers
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 ...
13
votes
7answers
8k views

What does imaginary number maps to physically?

I am taking undergraduate quantum mechanics currently, and the concept of an imaginary number had always troubled me. I always feel that complex numbers are more of a mathematical convenience, but ...
8
votes
2answers
624 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 ...
3
votes
5answers
336 views

Why is there a physical preference to real numbers?

In quantum mechanics, operators can only be observables if the eigenfunctions they operate on have real eigenvalues. If they are complex, I am told that, surely, some observable of a physical system ...
4
votes
3answers
967 views

What is the physical significance of $i=\sqrt{-1}$? [closed]

What is the physical significance of $i=\sqrt{-1}$?
6
votes
1answer
5k views

What is the purpose of the imaginary portion of the wave function?

I recently watched this video. I'm trying to learn about the origin of the wave function and therefore understand its use in the Schrödinger Equation. However at the end of the video I understood up ...

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