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

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SUMMARY

The discussion focuses on calculating the energies of four states for two interacting spin-1/2 particles using perturbation theory. The Hamiltonian is defined as Ho = -A(S_1z + S_2z) with a perturbation given by H1 = (S_1x * S_2x) - (S_1y * S_2y). Participants emphasize the necessity of analyzing perturbation terms to apply known operators such as S^2 or Sz effectively. The conversation highlights the importance of demonstrating initial attempts at problem-solving before seeking assistance.

PREREQUISITES
  • Understanding of quantum mechanics, specifically spin-1/2 particles.
  • Familiarity with Hamiltonian mechanics and perturbation theory.
  • Knowledge of angular momentum operators S^2 and Sz.
  • Basic skills in mathematical analysis of quantum states.
NEXT STEPS
  • Study perturbation theory in quantum mechanics, focusing on second-order corrections.
  • Learn about the properties and applications of angular momentum operators in quantum systems.
  • Explore examples of Hamiltonians for two-particle systems in quantum mechanics.
  • Review techniques for analyzing interaction terms in quantum mechanics.
USEFUL FOR

Students and researchers in quantum mechanics, particularly those studying two-particle systems and perturbation theory. This discussion is beneficial for anyone looking to deepen their understanding of quantum state energy calculations.

Penny
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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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@Penny , our homework helpers are not allowed to help until you show your attempt at a solution.
 
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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