NMR and the uncertainty principle: How to and how not to interpret homogeneous line broadening and pulse nonselectivity. IV. (Un?)certainty

Abstract

AbstractFollowing the treatments presented in Parts I, II, and III, I herein address the popular notion that the frequency of a monochromatic RF pulse as well as that of a monochromatic FID is “in effect” uncertain due to the (Heisenberg) Uncertainty Principle, which also manifests itself in the fact that the FT‐spectrum of these temporal entities is spread over a nonzero frequency band. I will show that the frequency spread should not be interpreted as “in effect” meaning a range of physical driving RF fields in the former, and “spin frequencies” in the latter case. The fact that a shorter pulse or a more quickly decaying FID has a wider FT‐spectrum is in fact solely due to the Fourier Uncertainty Principle, which is a less well known and easily misunderstood concept. A proper understanding of the Fourier Uncertainty Principle tells us that the FT‐spectrum of a monochromatic pulse is not “broad” because of any “uncertainty” in the RF frequency, but because the spectrum profile carries all of the pulse's features (frequency, phase, amplitude, length, temporal location) coded into the complex amplitudes of the FT‐spectrum's constituent eternal basis harmonic waves. A monochromatic RF pulse's capability to excite nonresonant magnetizations is in fact a purely classical off‐resonance effect that has nothing to do with “uncertainty”. Analogously, “Lorentzian lineshape” means exactly the same thing physically as “exponential decay,” and all inferences as to the physical reasons for that decay must be based on independent assumptions or observations. © 2008 Wiley Periodicals, Inc. Concepts Magn Reson Part A 32A: 373–404, 2008.