Undergrad Understanding the Absence of Rabi Oscillations in the Interaction Picture

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SUMMARY

The discussion centers on the absence of Rabi oscillations in the interaction picture of quantum mechanics, particularly when analyzing a two-level system's Hamiltonian in a rotating frame. It is established that this frame leads to an uncoupled Hamiltonian, resulting in the absence of dynamical phenomena such as Rabi oscillations. The conversation emphasizes the covariant formulation of quantum mechanics, ensuring that observable quantities remain picture-independent. A related thread on time-dependent unitary transformations of the Hamiltonian is referenced for further exploration.

PREREQUISITES
  • Understanding of the interaction picture in quantum mechanics
  • Familiarity with Hamiltonians in two-level systems
  • Knowledge of Rabi oscillations and their significance
  • Concept of covariant formulation in quantum theory
NEXT STEPS
  • Study the derivation of the interaction picture from the Schrödinger picture
  • Explore time-dependent unitary transformations of the Hamiltonian
  • Investigate the implications of covariant quantum mechanics on observable quantities
  • Learn about the mathematical framework of rotating frames in quantum systems
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Quantum physicists, students of quantum mechanics, and researchers interested in the dynamics of two-level systems and the interaction picture.

Jufa
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TL;DR
When working in the interaction picture one is free to choose the unitary transformation that seems helpful. How can I show that the dynamics of the problem are independent of such choice.
When working on the interaction picture you can show that in a certain rotating frame the Hamiltonian of a 2-level system (for example) becomes uncoupled. This implies that in such frame there are no Rabi oscillations or other dynamical phenomena, this seems weird to me and I would like to know how is this understood.
 
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Quantum mechanics can be formulated in a covariant way, i.e., such that the observable quantities (probabilities, expectation values of observables, cross sections in scattering theory etc. etc.) are by construction picture independent. There's a recent thread on this topic here at PF:

https://www.physicsforums.com/threa...ry-transformations-of-the-hamiltonian.979107/
A somewhat shortened derivation starting from the Schrödinger picture can be found on my posting #7 in this thread, though, as I said, you can formulate QT completely covariantly under "time-evolution-picture transformations" from the very beginning.
 
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