I know the usual reason is because we are considering millions and billions of spins in the Bloch description. However, while teaching my students quantum mechanics, i needed to explain quantum phenomena in NMR as application of QM in a very simple ways in which they can easily grasp; but a question appeared. 1. if we use a classical description to explain a quantum system, can we always regard the ensuing parameters as classical? (from Felix Bloch derived equations) 2. How many do quantum particles need become for a function describing them to become classical/macroscopic in nature?
Hello Michael. Your question is interesting. I suggest you check the "Magnetic Resonance Imaging Physical Principles and Sequence Design" by E. Mark Haacke. In this book there are several chapters that will help you find answers to your question. You can also email me directly specifying their need to guide you more better. Kind regards.
I don't love thinking about MR in classical theory for this reason - it confuses the bridge between vectors and the quanta contribution to the vector magnitude. My thought is that the macroscopic magnetization is likely due to the larger number of protons in the spin down state than those in the spin up state. Magnetic properties are influenced by spin and charge intrinsically. And so, a magnetic dipole is created for the proton with positive charge equal to electron charge but of opposite sign due to nuclear spin. Magnetic moment = paired proton and neutron. Without B0 or M, these guys are random, when placed in the field, antiparallel spins of high energy are in the spin down state, where as parallel spins are in the spin up state (low energy). For whatever reason, there are more protons in the low energy state (likely because of avogadro;s #), this contributes a huge amount to net and hence the net magnetic moment is in the spin down state or the vector direction of M. Essential physics of medical imaging explains this well chapter 12. Whereas Horowitz goes on and on about the vectors....Hope this helps... Jen
Thanks for your kind reply Takuya.
It is quite helpful. I quite agree it is not easy to answer. I have a professor who always says that the greatness of NMR is yet to be seen because the detailed physics of it is not yet known. I want to know how best to place the nature of M vector when explaining NMR to young students in a way that would not put them off before they got things started.
I actually attended a lecture where a tutor used the principles of NMR to explain why women (have to) talk more than men and it got me thinking; to what extent should physics be dragged into human behaviour and if this tutor is correct, will the consideration of the behavior of one person (which may be represented in some form of magnetization) be tantamount to single spin behavior or many spins?
I am sorry if i have not correctly order the question and the sentence but in my experience in quantum mechanics, a spin always need others to make a meaningful system!
I think the primary question has been answered already: both the classical and the quantum mechanical theory of NMR use a marcoscopic picture to discribe NMR phenomena. You can describe single nuclei as well - both classical and by QM - but that is not useful to understand and design NMR experiments.
I'd like to refer you to an excellent paper by Lars G. Hanson "Is quantum mechanics necessary for understanding magnetic resonance?" doi: 10.1002/cmr.a.20123
The Author examines the relationship between the QM and the classical theory of magnetic resonance in an excellent way. I think that might be helpful to you.
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