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the annihilation operator satisfies the equation [tex]\hat{a}[/tex]|n>=[tex]\sqrt{n}[/tex]|n-1> and [tex]\hat{a}[/tex]|0>=0

so the matrix of [tex]\hat{a}[/tex] should be

http://www.tuchuan.com/a/2010020418032158925.jpg [Broken]

and zero is the only eigenvalue of this matrix.

The coherent state is defined by [tex]\hat{a}[/tex]|[tex]\alpha[/tex]>=a|[tex]\alpha[/tex]>, yet [tex]\alpha[/tex]are not always equal to zero

Is there anything I forgot to consider?

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# Eigenvalue of the coherent state

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