Interaction Picture Doubts

[Jufa]

TL;DR Summary

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.

 

[vanhees71]

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.