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Classical Physics
Drude Model Permittivity Formula - e^iwt or e^(-iwt)?
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[QUOTE="vanhees71, post: 6037110, member: 260864"] Yeah, it's convention, and this involves some schizophreny even within the physics community alone (if you switch between physics E&M and electrical-engineering E&M textbooks, which often treat other subjects than the physics textbooks, you get completely confused). Usually the convention in full Maxwell theory is to choose the time dependence for harmonically evolving fields as ##\exp(-\mathrm{i} \omega t)##, while for circuit theory where you deal with integrated quantities like voltages and currents they choose ##\exp(+\mathrm{i} \omega t)##, which is of course nuts, because the integrated quantities are just the fields integrated over space after all. Why they choose a different convention, you must not ask me. I don't know; maybe they like to confuse students even more than the subject itself is confusing, and it's confusing enough for the beginner (particularly when the SI units are used, but that's another story). Then there are the various conventions concerning Fourier transformations of functions. In field theory, at least in the HEP community, the convention usually is like $$\psi(t,\vec{r}) = \int_{\mathbb{R}} \frac{\mathrm{d} \omega}{2 \pi} \int_{\mathbb{R}^3} \frac{\mathrm{d}^3 k}{(2 \pi)^3} \tilde{\psi}(\omega,\vec{k}) \exp(-\mathrm{i} \omega t+\mathrm{i} \vec{k} \cdot \vec{r}).$$ The inverse transformation then follows to be $$\tilde{\psi}(\omega,\vec{k})=\int_{\mathbb{R}} \mathrm{d} t \int_{\mathbb{R}^3} \mathrm{d}^3 r \psi(t,\vec{r}) \exp(+\mathrm{i} \omega t-\mathrm{i} \vec{k} \cdot \vec{r}).$$ It may well be that in other communities you have to convention used by Charles Link in #2. In the engineering literature it's also not uncommon to write ##\mathrm{j}## for the imaginary unit. [/QUOTE]
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Drude Model Permittivity Formula - e^iwt or e^(-iwt)?
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