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I have questions regarding my understanding of NMR and the mathematics of it. If anyone would take the time to read this, I would very much appreciate it. Please bear with me, I am a beginner. Thank you!

First, there is the question on how to model this phenomenon. Up till now I have used the Bloch equations. Recently I have come across the NMR pictured with a general Hamiltonian with zeeman, quadrupole, internuclear, and electron-nucleus terms. I have unable to comprehend this, is there a good reference to help explain this? How can I use a Hamiltonian to model the precession?

I would also like to know if there are any references to NMR experiments dealing with problem of inhomogeneity of the static field, and offsets in excitation rotations (the spins are not rotated as expected since the field changes at different depths of the sample).

Thank you.

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# NMR mathematics

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