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To calculate the line profile due to natural broadening it is common to assume that a decaying atom produces an electric field of the form: $$E(t)=E_0 e^{-t\gamma}\cos(\omega_0t)$$ as stated e.g. here (link to Google Books).

Here is my problem, I thought that on decaying an atom would release a single photon not a continuous wave; so why can we assume this form of electric field and where does it come from?

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I feel that it is due to the wave-particle duality, where photons can exist as both a particle and a wave. In this case then, a single photon in itself also produces a wave (you can check out Young's experiment on proving wave-particle duality, where even a single electron proved to have created a wave). Hence, this electromagnetic wave induces an electric field, and therefore even with a single photon, an electric field can still be created.

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