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

In summary, the conversation is about the derivation of the force acting on an atom in the Heisenberg picture. The disagreement arises when the Hamiltonian is said to only include the interaction between the atom and the EM-field, as the speaker believes that other parts of the Hamiltonian should also be considered. However, it is later determined that the dipole interaction is the only part with spatial dependence, leading to the conclusion that the other parts can be ignored.
  • #1
Niles
1,866
0
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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  • #2
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.
 

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

1. What is the Heisenberg picture of quantum mechanics?

The Heisenberg picture is one of two common formulations of quantum mechanics used to describe the behavior and properties of subatomic particles. In this picture, the observables (such as position, momentum, and energy) of a system are treated as fixed values, while the operators (such as the Hamiltonian operator) that represent these observables evolve over time.

2. How does the Heisenberg picture differ from the Schrödinger picture?

In the Schrödinger picture, the states of a system are treated as evolving over time, while the observables are fixed. This means that the operators representing the observables do not change, but the states of the system do. In contrast, the Heisenberg picture treats the states as fixed and the operators as evolving over time.

3. Why is it important to understand force on an atom in the Heisenberg picture?

Understanding force on an atom in the Heisenberg picture is important because it allows us to accurately describe and predict the behavior of atoms and molecules at the subatomic level. This is important for a wide range of applications, from developing new materials to understanding chemical reactions.

4. How does the Heisenberg picture account for uncertainty in the position and momentum of particles?

In the Heisenberg picture, the uncertainty principle is accounted for by the commutation relations between the position and momentum operators. These relations show that it is impossible to simultaneously know the exact position and momentum of a particle, and that the more precisely we measure one, the more uncertain the other becomes.

5. Can the Heisenberg picture be used to describe macroscopic objects?

No, the Heisenberg picture is only applicable to the behavior of subatomic particles. Macroscopic objects are governed by classical mechanics, which does not take into account the principles of quantum mechanics. However, the principles of quantum mechanics can still have indirect effects on macroscopic objects through phenomena like superposition and entanglement.

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