Understanding Force on an Atom in the Heisenberg Picture of Quantum Mechanics

[Niles]

Hi

In the following paper (on page 5) is the standard derivation of the force acting on an atom, whose center-of-mass motion is described classically. What I don't understand is the step taken from (5) to (6).

The QM-version of the force is defined using Heisenbergs Equation of Motion (so we are in the Heisenberg picture). Then they write that the force is just the spatial derivative of the Hamiltonian. All OK so far. Then they say that the Hamiltonian is only the part describing the interaction between the atom and the EM-field. This is what I don't agree with. We are in the Heisenberg picture, not the Interaction picture so we need to take into account more than just the interaction Hamiltonian?


Niles.

 

[Niles]

Ah, I actually think I might be right here. However, the reason why they end up only with the dipole interaction is because all the other parts if the Hamiltonian don't have any spatial dependence.