Hilbert space methods provide one possible answer to this question.

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.

It may take the form of a Hilbert space.

The Hilbert space for the single site is with the base .

The strong convergence of a sequence in a Hilbert space.

In this article we assume that Hilbert spaces are complex.

The state can be expanded in any convenient basis of the Hilbert space.

This space is complete and we get a Hilbert space.

The space of states is not a Hilbert space (see below).

This idea can be used to represent operators on Hilbert spaces, for example.

The given space is assumed to be a Hilbert space.

The methods use the theory of bounded operators on Hilbert space.

Of these the spin factors can be constructed very simply from real Hilbert spaces.

Dynamics are also described by linear operators on the Hilbert space.

See also Hilbert space for a more rigorous background.

It is however much more general as there are important infinite-dimensional Hilbert spaces.

Given a system, the possible pure state can be represented as a vector in a Hilbert space.

An important example is a Hilbert space, where the norm arises from an inner product.

A complete space with an inner product is called a Hilbert space.

Let be an unknown quantum state in some Hilbert space (and other states have their usual meaning).

This space has a positive definite form, making it a true Hilbert space.

This means it is not a Hilbert space.