In a coherent state defined by [tex] |\alpha\rangle = \exp{\left(-\frac{|\alpha|^2}{2}\right)}\exp{\left(\alpha \hat{a}^\dagger\right)} |0\rangle[/tex] there is a definite phase associated with the state by [tex] \alpha = |\alpha| \exp{\left(i\theta\right)} [/tex] where the number operator and phase operator are conjugates, [tex] -i\partial_{\theta} = \hat{n}. [/tex] The meaning of the number operator is obvious but what is the significance of the phase in this state? What would be a consequence of picking a new phase for this state?(adsbygoogle = window.adsbygoogle || []).push({});

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# I What's the significance of the phase in a coherent state?

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