Fig. 1

(Color online) Plot of numerical solutions of Eq. (15) for $\mu=1$ and $l=1$. Boundary conditions are $M(r)$ using $M(r_i) = M(r_f) = 1/2$ for $r_i=0.22$ and $r_f=1$, here we fix $\theta_0 = \pi/4$. As close as one approaches the origin, where the dyon is located, the solution diverges."

Fig. 2

(Color online) Plot of numerical solutions of Eq. (15) for some values of $\theta$. In these solutions we consider $\mu=1$, $l=1$, and $N=0$. Boundary conditions are $M(r)$ using $M(r_i) = M(r_f) = 1/2$ for $r_i=0.22$ and $r_f=1$, for $\theta$ between $10^\circ$, and $140^\circ$ approximately, there is a continuum of radial solutions."

Fig. 3

(Color online) Effective potentials calculated using solutions of Eq. (15) with $M(r_i) = M(r_f) = 1/2$ for $\theta_0 = \pi/4$, $r_i=0.22$, and $r_f=1$. The three curves for $N=0,1,2$ (blue, yellow and green) are overlapped. Parameters are $\mu=l=1$."

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 $eQ=-1$."

Table 1

Summary of the mapping between charge-dyon and PDM systems in the non-relativistic and relativistic regimes, respectively."