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Ground state of hamonic oscilator

  1. Mar 24, 2015 #1

    naima

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    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 Wigner functions:
    Where is the error?
    Thanks.

    Edit sorry, in the link the W function is for a (n = 1) Fock state. So no more problem.
     
    Last edited: Mar 24, 2015
  2. jcsd
  3. Mar 24, 2015 #2

    vanhees71

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    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.
     
  4. Mar 24, 2015 #3

    naima

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    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.
     
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