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- Thread starter nolanp2
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strangerep

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i've just encountered coherent states while studying the quantum oscillator, and i'm trying to understand some of the semiclassical properties of them. can someone give me a brief description of what they represent in the system

In this case, coherent states can be described in three equivalent ways.

1) They saturate the Heisenberg uncertainty relation (i.e., minimize the simultaneous

uncertainty in position and momentum). One therefore says that they're "as classical

as possible".

2) They are eigenstates of the annihilation operator.

3) They can be generated by applying a certain operator from the Heisenberg

group to the vacuum state.

In simple cases, it often happens that coherent states evolve intoand of how they vary in time?

coherent states.

For a pedestrian amusing introduction to such things, try the old spr conversation

between Michael Weiss and John Baez on "Photons, Schmotons". It's available

in edited form at: http://math.ucr.edu/home/baez/photon/schmoton.htm

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strangerep

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They are not identical. The set of coherent states forms an (overcomplete) basis for the

oscillator will be a coherent state for all t? are all coherent states identical?

Hilbert space of states of the oscillator. (I.e., any state in the Hilbert space can be

expressed as an integral over the coherent states. "Over"-complete means they are

not mutually orthogonal.)

Try Wikipedia for a bit more info.

If you have access to a University library, try the book by Mandel & Wolf

"Optical Coherence & Quantum Optics". Their section on coherent states

explains quite a lot of interesting stuff.

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