# Zeeman Splitting

INCORRECT. Zeeman splitting is part of a quantum mechanical (QM) description of MRI, and this answer is a dangerous mix of the QM and classical approaches. In fact, spins do not reside exclusively in the Zeeman energy levels, and so we cannot say that (classical) parallel and antiparallel states equate to the Zeeman levels.

Zeeman spitting is part of the QM description of MRI. Try again.

INCORRECT. Zeeman splitting does not describe transitions from one spin state to another. Incidentally, transition of spins between discrete states is part of a classical description of MRI (the quantum mechanical description does not include such transitions). Try again.

Zeeman splitting

CORRECT. When placed in an external magnetic field, the direction of angular momentum arising from nuclear spin is quantized (it can only take certain values). This results in discrete energy eigenstates. (Without an external magnetic field these states collapse into one state.) This quantization of angular momentum is described by only allowing certain values of the azimuthal quantum number m_{s}. For hydrogen m_{s} = ±½. These two values of m_{s} correspond to two energy eigenstates separated by a quantum of energy equal to ~~h~~ω_{0}. The splitting of the energy level into two like this—in the presence of a magnetic field—is Zeeman splitting.

Do not be confused by the fact that we discuss specific energy levels (eigenstates). It may be confusing to equate these eigenstates to spin up and spin down states, or parallel and antiparallel spin orientations (both of which are part of the classical description of MRI). Eigenstates are used when describing observable population differences in the state of an *ensemble* of spins. In the quantum mechanical description of MRI, spins don't reside in the Zeeman eigenstates, but are in fact in superpositions (linear combinations) of both states.

Note that Zeeman splitting is a quantum mechanical effect, and without it MRI and NMR would not exist. The equivalent population difference which occurs between the two energy eigenstates results in the net magnetisation in a sample.

The QM explanation goes on to describe net spin polarisations which result in a net magnetisation vector, and the state of an individual spin occupying a specific energy state or "pointing" one way or another becomes less meaningful. In spite of this, we still use diagrams with spins "pointing" and occupying energy levels in an attempt to communicate only the notions of spin polarisation density and superposition coefficients, respectively.

Further reading on this topic:

Books: Spin Dynamics p244, MRI: Physical Principles & Sequence Design p71, Q&A in MRI p22