These can produce new coherent states and allow us to move around phase space.
The construction of coherent states using group representations described above is not sufficient.
A coherent state is not a point in the optical phase space but rather a distribution on it.
It is possible to define operators to move the coherent states around the phase space.
Moreover, these coherent states may be generalized to quantum groups.
This work led to the concept of coherent states and the development of the laser.
They can also be defined as squeezed coherent states.
Thus, the vectors constitute a family of generalized coherent states.
For application to lasers, the amplification of coherent states are important.
By construction, P for a coherent state is simply a delta function: