Heisenberg picture ↩

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created: 2021-11-09 13:19:32
modified: 2022-01-16 18:05:53

Where is the wavefunction of the Schrödinger picture. We can observe that the states are stopped here.

Operators

(The operators are the time evolution operators from Schrödinger picture)
With this, the transformation of an operator becomes:

This means that even time independent operators in the Schrödinger picture become time dependent in the Heisenberg picture.

Time derivative

We can take the time derivative of an operator the following way:

Where of course the Hamiltonian operator in the Heisenberg picture is the following:

And

Time dependence of the hamiltonian operator

It is easy to see that the Hamiltonian operator is time independent in the Heisenberg picture if it is time independent in the Schrödinger picture as well: