Where a and b are time-dependent quantum amplitudes incorporating "harmonic oscillations" of the two principal states |+½> and |-½>. The phases of the million+ other spins are all randomly dispersed and cancel each other out, so only the few "coherent" ones contribute to vector M.įrom a quantum mechanical perspective, recall from a previous Q&A that the wave function describing the hydrogen nucleus could be written as: Thus what was a slightly skewed spin energy distribution in the longitudinal direction has become "phase coherence" in the transverse plane after the RF-pulse.Īfter the 90 °-pulse only a small fraction of spins are actually "pointing" in the M direction. The only effect of the 90 °-pulse is to rotate this entire spin-distribution including M into the transverse plane. When we summed them all together, we obtained M, the net magnetization (technically, a statistical "expectation") that pointed due North.Īt equilibrium prior to the RF-pulse the spin system has a net population difference representing a form of thermodynamic "order". On the average, however, more were pointing north than in any other direction. Because of thermal interactions (the dryer rotating), the individual compass needles ended up pointing in all possible directions. In this analogy, individual spinning nuclei were likened to tiny compass needles each seeking to point to the north pole (symbolized by the North Star, Polaris).
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