# Longitudinal Magnetisation (QM)

INCORRECT. Spins do not occupy specific energy levels in the QM description of MRI. See Zeeman eigenstates.

This incorrect answer mixes the classical and QM descriptions of MRI. Try explaining *transverse* magnetisation using the picture of spins occupying only specific energy levels!

Net polarisation against the field (the degree of polarisation is greatly exaggerated).

CORRECT. Diagrams indicating spin polarisation are a physical interpretation of the relevant quantum mechanical equations (not given here). Partial alignment of spins in any particular direction equates only to an overall spin polarisation density, *not* individual spin directions. For longitudinal net magnetisation, no individual spin is depicted fully aligned with or against the field—accordingly the relative population of eigenstates does not mean spins occupy *that* energy level (spins are actually in a superposition of states). An energy level diagram is intended to indicate *only* that an *observable population difference* exists upon measurement.

When there is a net spin polarisation with or against the external magnetic field, we can *imply* that a number of particles are in the higher energy state as "spin down" or "antiparallel" with respect to the external magnetic field B_{0}, though this is not strictly true. Similarly, we can imply that a number of particles are in the lower energy state, referred to as "spin up" or "parallel" with respect to B_{0}. In fact, assigning spins a parallel or antiparallel direction is only a way of describing the *observable population difference* between the two energy *eigenstates*, and any notion of alignment of spins with B_{0} is only a *physical interpretation* of the relevant quantum mechanical equations (not given here).

The notion of a spin pointing this way or that should not be over-interpreted; the "spin polarisation arrows" do not behave like ordinary vectors. (For instance, an arrow aligned with B_{0} does not mean that the angular momentum perpendicular to B_{0} is zero; the angular momentum in that (transverse) plane is *undefined*.) When energy is introduced into the spin system, mathematical superposition coefficients change which manifests in a change in the apparent (measured) population of the two spin states. (Superposition coefficients are part of quantum mechanical equations—not given here—which describe the probability that a spin will be found polarised in one or the other eigenstates upon measurement.)

Further reading on this topic:

Books: Spin Dynamics p279, Q&A in MRI p22