Calculate the energies of all 4 states up to 2nd order

In summary, the conversation is about a problem involving two interacting particles with spin 1/2 each and a Hamiltonian of Ho=-A(S_1z + S_2z). There is also a perturbation term of H1={(S_1x)*(S_2x) - (S_1y)*(S_2y)} and the question is asking for the energies of all 4 states up to 2nd order. The person seeking help has shown some progress but is stuck on how to analyze the perturbation terms using S^2 or Sz.
  • #1
Penny
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0
Moved from a technical forum, no template.
Hi,
I'm dealing with the following problem. I hope someone could help me with it.
Problem is about 2 interacting particles (spin: 1/2 each), with Hamiltonian Ho=-A( S_1z + S_2z) and perturbation H1={(S_1x)*(S_2x) - (S_1y)*(S_2y)}. The question asks to calculate the energies of all 4 states up to 2nd order.
 
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  • #2
:welcome:

@Penny , our homework helpers are not allowed to help until you show your attempt at a solution.
 
  • #3
This is what i managed to do so far. I'm stuck with the perturbation terms on how to analyze them further so i can use S^2 or Sz that are already known.

20180823_225609.jpg


(sorry about the missing attempt at a solution, i wasn't aware)
 

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Related to Calculate the energies of all 4 states up to 2nd order

1. How do you calculate the energies of all 4 states up to 2nd order?

To calculate the energies of all 4 states up to 2nd order, you can use the perturbation theory method. This involves expanding the Hamiltonian into a series and solving for the energy levels up to the desired order.

2. What is the significance of calculating the energies up to 2nd order?

Calculating the energies up to 2nd order allows for a more accurate prediction of energy levels and transitions between states. It takes into account the effects of perturbations on the system, resulting in a more precise calculation.

3. Can you provide an example of calculating energies up to 2nd order?

As an example, let's consider a hydrogen atom in an electric field. By using perturbation theory, we can calculate the energy levels up to 2nd order and determine how the electric field affects the energy levels of the atom.

4. Are there any limitations to calculating energies up to 2nd order?

Calculating energies up to 2nd order assumes that the perturbations on the system are small and do not significantly alter the energy levels. If the perturbations are too large, higher order calculations may be necessary to accurately predict the energy levels.

5. How does calculating energies up to 2nd order compare to other methods?

Calculating energies up to 2nd order is a common method used in perturbation theory and is often more accurate than 1st order calculations. However, higher order calculations may be needed for more complex systems or larger perturbations.

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