Stationary spin

Figure 5. A stationary spinning cone. The polar vector corresponds to the polar axis of the cone, and the axial vector to the direction of spin. Time reversal (T) changes the sense of chirality of enantiomorphous systems (a) and (b) in terms of the helicity generated by the product of the two vectors, (a) is right-handed and (b) is left-handed. The left-handed system (c) [the enantiomorph of (a) and the homomorph of (b)] is obtained either by space inversion (P) of (a) or by rotation of (b) by 180° (Rn) about an axis perpendicular to the polar axis.

Objects that exhibit -invariant enantiomorphism are either immobile or undergo a motion that can be reduced to a screw displacement (as exemplified in Figure 4). Objects that exhibit 7-noninvariant enantiomorphism behave effectively like stationary spinning cones (cf. Figure 5). We now show that all these objects belong to chiral groups. 

Figure 7. Illustration of symmetry. Top Mirror images of an achiral (C h symmetry) construction. As the number (n) of striations approaches infinity, the symmetry of the constructions approaches C< h in the limit. Bottom Stationary spinning cylinders with C-i, symmetry.

Transforming to the rest-frame of the moving beam-particles the quantum mechanics of a spin-1/2 particle traversing the spin-precession apparatus is equivalent to the quantum mechanics of a stationary spin-1/2 particle perturbed by a sequence of external field pulses. Such a system was investigated by Luck et al. (1988). It was found that the quantum dynamics of a spin-1/2 particle perturbed by a sequence of pulses arranged according to a Fibonacci sequence is indeed very complicated. 

Diffusion and imaging experiments rely on the imposition of controlled field gradients to provide a coordinate system. Take, for example, the idealized one-dimensional system shown in Fig. 17, composed of two identical stationary spins. During a normal NMR experiment, the field is homogeneous across the sample, and the black and white spins precess at the same frequency, appearing at the same chemical shift (Fig. 17a). If, on the other hand (Fig. 17b), the field is varied linearly across the sample, the two spins do not experience the same magnetic field, and so resonate at different frequencies. They therefore appear as distinct peaks in the spectrum. 

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