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Illustration Plane wave in a complex plane

Level 3
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.
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A one-dimensional plane wave with amplitude \(A\), wave number \(k\) and angular frequency \(\omega\) represented as a complex exponential function:\[ \mathit{\Psi}(x,t) ~=~ A \, e^{\mathrm{i}\,(k\,x - \omega\,t)} \]

This is represented in a complex plane as a vector. Its length corresponds to the ampltude \(A\) and the angle \(\varphi\) between the \(\mathit{\Psi}\)-vector and the real axis corresponds to the phase \( k\,x - \omega\,t \). As time passes, the phase changes and the vector rotates (here: clockwise).

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  • License: CC BY 4.0This illustration may be used with indication of the copyright!
  • Copyright: © 2020
  • This illustration was uploaded by FufaeV on .
  • This illustration was updated by FufaeV on .

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