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**lowering**operator ##a##

[tex]|\alpha\rangle=e ^{-\frac{|\alpha|^2}{2}}\sum^{\infty}_{n=0}\frac{\alpha^n}{\sqrt{n!}}|n \rangle [/tex], where ##\{|n \rangle\}## are eigenstates of energy operator. What is the case of state ##|0 \rangle##?

[tex]a|0 \rangle=0|0 \rangle=0.[/tex]

So, ##|0 \rangle## is eigenstate of

**lowering**operator. But how to get that from

[tex]|\alpha\rangle=e ^{-\frac{|\alpha|^2}{2}}\sum^{\infty}_{n=0}\frac{\alpha^n}{\sqrt{n!}}|n \rangle ?[/tex]