Ground state of hamonic oscilator

[naima]

When i take a coherent state ##|\alpha>## if ##\alpha -> 0## then the limit is the Fock state for n = 0. so ##|n = 0> = |\alpha = 0>##
The problem is that they seem to have different http://www.iqst.ca/quantech/wiggalery.php:
Where is the error?
Thanks.

Edit sorry, in the link the W function is for a (n = 1) Fock state. So no more problem.

 

[vanhees71]

I don't understand your question. Among other definitions, you can define a coherent state of a given mode as an eigenvector of the corresponding annihilation operator
$$\hat{a} |\alpha \rangle=\alpha |\alpha \rangle,$$
where ##\alpha \in \mathbb{C}##. For ##\alpha=0## that's the definition of the "vacuum" (absence of the considered mode). Thus also the vacuum is a special coherent state.

 

[naima]

I had in mind the fact that for an integer ##\alpha## the Fock state ##|\alpha>## is just one of the terms of the serie of the coherenet state ##|\alpha>##.
I did not saw that for 0 the serie has only one term.