# Questions tagged [complex-numbers]

Numbers of the form $\{z= x+ i\,y:\;x,\, y\in\mathbb{R}\}$ where $i^2 = -1$. Useful especially as quantum mechanics, where system states take complex vector values.

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### Square root of -1 vs many-worlds [closed]

I am not sure if this is a dublicate. When I see the suggested questions about the subject they seem to take the concept more or less for granted. Sometimes we may benefit from seemingly unrealistic ...
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### Why do physicists like to put the imaginary unit $\:i=\sqrt{-1}\:$ everywhere?

There are many disagreements of convention between mathematicians and physicists, but a recurring theme seems to be that physicists tend to insert unnecessary factors of $i = \sqrt{-1}$ into ...
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### Eigenvalues of antiunitary operators

I have sometimes come across the statement that antiunitary operators have no eigenvalues. For example, on page 34 in the book "Topological Insulators and Topological Superconductors" by ...
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### Why not just complex conjugate bras and kets instead of Hermitian conjugate?

I read that one equation involving bras, kets and operators, implies another equation (its transpose conjugate), analogous to how one equation involving complex numbers implies its complex conjugate ...
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### Does swapping “$i$” with “$-i$” change a physical theory?

Mathematically speaking, "$i$" and "$-i$" are the two roots of the equation $x^2+1=0$ and it seems to me at least that there is no obvious way of distinguishing between them. Thus, ...
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### Do we necessarily need real number for quantum? [closed]

In the quantum mechanics, one asked if the complex number was necessary? A typical answer was that it was not, or that it's simple direct product of real numbers. However, consider rational number to ...
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### Complex exponential method of solving differential equations

In the twenty third Feynman lecture, the solution of the following differential equation is discussed: $$\frac{d^2 x}{dt^2} + \frac{kx}{m} = \frac{F}{m}$$ AFter 'complexifying' this differential ...
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### How to find the input impedance of a woodwind instrument? (playing frequency of a woodwind instrument)

I'm trying to reproduce the model described in this paper https://hal.archives-ouvertes.fr/file/index/docid/683477/filename/clarinette-logique-8.pdf. The logical clarinet is a succession of 18 ...
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### The use of complex fields in electromagnetism

Virtually all treatments of electromagnetic wave propagation, and in particular of monochromatic plane waves, use basic complex analysis to simplify calculations. I am comfortable with these ...
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### Derivative of a complex potential for the $\lambda \Phi^{4}$-model

A charged scalar particle is described by a complex field $\Phi(x) = \phi_{1}(x)+i\phi_{2}(x)$. Consider a Lagrangian of the $\lambda \Phi^{4}$-model whose potential in the Euclidean action is given ...
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