The ground state for a particular oscillator cannot be lowered.
The state in which **all the oscillators are in the ground state is called the vacuum state**and can be written simply as
.
We can generate any state we want by applying raising operators to the vacuum state.

The factorial on the bottom cancels all the we get from the raising operators.

Any multi-photon state we construct is **automatically symmetric under the interchange of pairs of photons**.
For example if we want to raise two photons out of the vacuum, we apply two raising operators.
Since
, interchanging the photons gives the same state.

So the fact that the

Jim Branson 2013-04-22