That is the action on the Hilbert space - change basis to p at time t.
In this representation, the group elements act on a particular Hilbert space.
These do not, technically, belong to the Hilbert space itself.
The same construction can be applied also to real Hilbert spaces.
The state can be expanded in any convenient basis of the Hilbert space.
The Hilbert space for the single site is with the base .
It may take the form of a Hilbert space.
The strong convergence of a sequence in a Hilbert space.
In this article we assume that Hilbert spaces are complex.
This space is complete and we get a Hilbert space.