Fig. 4 (Color online) Plot of analytical solution of Eq. (19) given by Eq. (24). In Fig. 4(a) we plot the mass distribution which would produce the pure Dirac magnetic monopole. Observe that the mass increases as one approaches the Dirac string which is located at $\theta=\pi$.In Fig. 4(b) we plot the mass distribution which would produce the Dirac magnetic monopole without the string using the well-known Wu-Yang construction.[21] The above position-dependent mass reproduces exactly the eigenfunction of a relativistic charge-dyon system with $\mu=1$, $l=0$, $N=1$, and $eQ=-1$.
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