Quantum Mechanics and MRI
Short answer? Almost none. The little bit about Zeeman splitting is helpful. But I would encourage forays into the non-intuitive world of quantum mechanics (QM) as the student has motivation. For clinical work the quantum mechanical description of MRI is unnecessary. But bear it in mind that without QM MRI wouldn't exist. MRI is essentially the manipulation of "spins" within a strong magnetic field, which then return to an equilibrium state. That a particle has "spin" is actually a mathematical description of the quantum mechanical nature of the particle - that happens to behave mathematically like spin - rather than a conceptual one (a sphere spinning on an axis). It is easy to imagine a positively charged sphere (e.g. the proton) of finite size (radius ~10-14 m), finite mass (~10-27 kg) and a net electric charge (~10-19 C) spinning, and therefore possessing a magnetic dipole moment. However, the electron (finite mass ~1/1836 proton mass) also possesses spin, yet it is indicated to be a point-particle with no spatial extent. Imagining the electron "spinning" becomes somewhat difficult.
We can continue to think of spin as the angular momentum of a spinning particle, as proposed originally for large atomic nuclei (by Pauli in 1924) and the electron (Uhlenbeck in 1925), because this approach leads to the correct results and no contradictions as far as magnetism and magnetic resonance are concerned. It is, however, intellectually sterile. Paul Dirac published a paper in 1928 in which the existence of spin emerges naturally in a relativistically correct formulation of quantum mechanics. Unfortunately there is no macroscopic picture that we can describe which properly explains the true quantum mechanical nature of matter. The only language that can do it is maths. In other words, to understand the QM basis of MRI, expect quite involved maths!