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- W1999513708 abstract "A quantum-mechanical context is used to discuss the advantages offered by a Euler–Rodrigues (ER) parameterization of the rotation implicit in the propagators of spin-½ and spin-1 systems. To appreciate these advantages, we begin with a spin-½ propagator, using either a rotation angle–axis {Φ, nˆ} or a Euler angle {α, β, γ} parameterization of the rotation operator. The kinematic relations for the ER parameters and the Euler angles are then derived via the rotation operator approach, and used to compare the two parameterizations. As an illustration of the utility of the ER parameterization, the role of time symmetry in composite pulse design for spin-½ and spin-1 systems is elucidated. A phase-alternating composite pulse pair {π(I=½), π/2(I=1)} is considered, and well-established analogies are shown between the respective spin-½ and spin-1 propagators. Simple relationships among the phase and amplitude factors of the pulse pair are easily established using the respective ER parameters. ©1997 John Wiley & Sons, Inc. Concepts Magn Reson 9: 211–225, 1997" @default.
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- W1999513708 date "1997-01-01" @default.
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- W1999513708 title "Rotations in NMR: Part II. Applications of the Euler-Rodrigues parameters" @default.
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- W1999513708 doi "https://doi.org/10.1002/(sici)1099-0534(1997)9:4<211::aid-cmr2>3.0.co;2-1" @default.
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