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I was reading a book about electrodynamics.

the book said

we shall now consider the special case when 'the scalar potential' and the field component depend harmonically on the $z$ coordinate (along a steady magnetic field), i.e., when 'scalar potential' and the fields contain one of the following functions (or a linear combination of them)
$\exp(i\beta z)$, $\exp(-i\beta z)$, $\sin(\beta z)$, $\cos(\beta z)$.

I don't understand what 'harmonic dependence' means. Does it mean kind of 'periodic'? or 'harmonic function' that satisfies Laplace's equation?

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  • $\begingroup$ Given that the author lists only periodic functions, it seems he uses 'harmonic' in the meaning of 'periodic'. $\endgroup$ – Thomas Fritsch Jun 10 at 8:44
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Based on your citation from the book, I think the definition is given:the fields contain one of the following functions (or a linear combination of them) exp(iβz), exp(−iβz), sin(βz), cos(βz).

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