where D(α) = e αâ † -α * â = e -|α| 2 /2 e αâ † e -α * â is the displacement operator (analogous to Eq. 120 where the second equality comes from the Glauber formula) and |0⟩ is the vacuum state. By operating the displacement operator on the vacuum state |0⟩, the coherent state |α⟩ can be expressed as