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In my course on quantum mechanics, we have seen that coherent states look classical. Since the expectation value of the electric field is similar as for the classical expression. Furthermore they look classical since the variance of position and momentum is the same as in the vacuum ground state. I understand the mathematics to get to this, however I am wondering whether there is some intuition on why eigenstates of the annihilation operator look classical?

Thanks in advance

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If one reviews the procedure of the electromagnetic field quantization, the field are given by the expressions like $$ E\propto \sum_k\left(a_ke^{ikx}+a_k^\dagger e^{-ikx}\right), $$ where $a_k, a_k^\dagger$ are the complex amplitudes of the fields. Quantization consists in declaring these amplitudes operators, obeying a commutation relation - however, it is logical /consistent to expect that in the classical limit the quantized field should still resemble the classical field, as per correspondence principle.

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