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

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The discussion centers on the derivation of force acting on an atom within the Heisenberg picture of quantum mechanics, specifically addressing the transition from equations (5) to (6) in a referenced paper. The force is defined as the spatial derivative of the Hamiltonian, which is claimed to only include the interaction between the atom and the electromagnetic field. However, there is contention regarding whether the full Hamiltonian should be considered, as the Heisenberg picture typically encompasses more than just the interaction Hamiltonian. The conclusion drawn is that the dipole interaction is the primary contributor due to the lack of spatial dependence in other Hamiltonian components.

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Niles
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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.
 
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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.
 

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