Heisenberg picture

Let's work in the Heisenberg picture where x, b and are functions of time.

The following commutation relations are postulated in the Heisenberg picture.

In the Heisenberg picture, the density matrix does not change with time, but the operators are time-dependent.

Here represents the initial density matrix, and the operators are expressed in the Heisenberg picture.

This approach is called the Heisenberg picture.

The coherent state is an eigenstate of the annihilation operator in the Heisenberg picture.

The two most important are the Heisenberg picture and the Schrödinger picture.

Alternatively, the Heisenberg picture can be used where the time dependence is in the operators rather than in the states.

In the Heisenberg picture, the derivation is trivial.

The Heisenberg picture moves the time dependence of the system to operators instead of state vector.

The Heisenberg picture supplies a direct link to quantum thermodynamic observables.

Consider the case of a purely quantum channel Ψ in the Heisenberg picture.

Let be a channel in the Heisenberg picture and be a chosen ideal channel.

Lorentz invariance is manifest in the Heisenberg picture, since the state vectors do not single out the time or space.

Lorentz invariance is manifest in the Heisenberg picture.

The idea is to look for states in the Heisenberg picture that in the distant past had the appearance of free particle states.

While the state vectors are constant in time in the Heisenberg picture, the physical states they represent are not.

As a final aside, the above equation can be derived by considering the time evolution of the angular momentum operator in the Heisenberg picture.

This approach is somewhat reminiscent of a change from the Schrödinger picture to the Heisenberg picture.

The Heisenberg picture is employed henceforth.

In the Heisenberg picture, the X and P operators satisfy the classical equations of motion.

Therefore, in the Heisenberg picture, if the classical information is part of, say, the input, we would define to include the relevant classical observables.

The Heisenberg picture of time evolution accords most easily with RQM.

The Heisenberg picture is an alternative mathematical formulation of quantum mechanics where stationary states are truly mathematically constant in time.

Allow time-dependence to denote the Heisenberg picture observables: