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The four postulates of the Quantum Mechanics do not talk anything about the reference frame in which the Hamiltonian is built and also the measurements that we do. Is it that the postulates are valid in a Newtonian inertial reference?

Moreover, when we find the Hamiltonian in an NMR to change the orientation of the magnetization vector, we shift to the rotating reference frame to make the Hamiltonian time independent. This is done by applying the normal time dependent rotation along the z-axis(the direction of the static magnetic field) which at the end cancels out giving the same Hamiltonian as in the stationary lab frame. How is it that the laws of the quantum mechanics are exactly the same in both the lab and the rotating frame(rotating at the Larmor Frequency) of the NMR while it is never so in the case of the Newtonian Mechanics?

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