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In this lecture, I introduce the radiofrequency Hamiltonian for radiofrequency pulses. These are largely used in NMR spectroscopy and MRI to interact with nuclear spins. Given the oscillating nature of the radiofrequency radiation, such a Hamiltonian has a time dependence that may complicate the spin dynamics. To remove such a time dependence, I use the interaction frame transformation introduced in Lecture 5 to define a rotating frame. I then discuss the effects of on- and off-resonance radiofrequency pulses and calculate the magnitude of the Bloch–Siegert shift generated by a counter-rotating term in the radiofrequency Hamiltonian.

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