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In quantum mechanics, what exactly is a coherent state, and how does it differ from other states?

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Did you look at the wikipedia page en.wikipedia.org/wiki/Coherent_state ? – Qmechanic♦ May 25 '11 at 21:05
@Qmechanic yup! – wrongusername May 26 '11 at 0:43

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A coherent state is a state that is not an energy eigenstate, so the observables vary in time, but the uncertainty of the canonical conjugates (position and momentum) stays constant - unlike, for instance, in an ordinary wave packet moving in free space: this "floats away", the position uncertainty gets ever bigger and bigger.

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Did you look at the wikipedia page en.wikipedia.org/wiki/Coherent_state ? Did you look at Qmechanic's comment? Can you justify this being the most important feature of a coherent state to keep in mind when reading something like the Wikipedia entry for someone new to the topic? – Peter Morgan May 25 '11 at 21:43
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@Peter: I don't claim this to be the most important feature - there is no such thing anyway, as there are many equivalent definitions. It's just a description that I consider easy to understand, and it allows this simple counterexample to see what sets "ordinary" states apart from coherent states. – leftaroundabout May 25 '11 at 21:56
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A coherent state isn't the same thing as a squeezed state.

$$a|z\rangle = z|z\rangle$$

is a coherent state.

$$(\alpha x + i\beta p)|z\rangle = z| z \rangle$$

is a squeezed state.

For both, the product of uncertainties is minimized, but the former is more related to the Hamiltonian.

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