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Now the Dirac eigenfunctions on $\mathbf{R}^3$ are not compactly supported which makes it harder to interpret the Dirac wavefunctions.  Dirac eigenfunctions on a compact manifold have a better chance of being localized.  On the round three-sphere $S^3$ the eigenspinors can be computed exactly and the localization can be checked directly.  We can make a reasonable conjecture that for perturbations of the great sphere embedded in $S^4(1/h)$ mildly the same localization holds.