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This is the second in a series of two papers presenting a solution toHilbert's 12th problem for real quadratic function fields in positivecharacteristic, in the sense of proving an analog of the Theorem ofWeber-Fueter. We also offer a conjectural treatment of the number field caseusing quasicrystal counterparts of the constructions used in function fields.  Let $K/\mathbb{F}_{q}(T)$ be quadratic and real, $\mathcal{O}_{K}$ theintegral closure of $\mathbb{F}_{q}[T]$ in $K$. To each $f\in\mathcal{O}_{K}^{\times}$ we associate an order$\mathcal{O}_{f}\subset\mathcal{O}_{K}$ for which$\mathcal{O}_{f}^{\times}/\mathbb{F}_{q}^{\times} =\langle f\rangle$, andconsider the ideals $\mathfrak{M}_{f}\subset\mathcal{O}_{f}$ with $f\equiv1\mod \mathfrak{M}_{f}$. The union of the ray class fields$K_{\mathfrak{M}_{f}}$, as one varies over $f$ and $\mathfrak{M}_{f}$, is themaximal abelian extension of $K$ split over the two primes dividing $\infty$.  To $f$ we also associate the quantum Drinfeld module $\rho^{\rm qt} $: ageneralization of Drinfeld module whose elements are multi-points. Given$\mathfrak{M}_{f}$ a modulus in the family described above, we may define themodule of quantum torsion points $\rho^{\rm qt}[\mathfrak{M}_{f} ] $. The maintheorem of the paper is that $K_{\mathfrak{M}_{f}}$ is generated over theHilbert class field $H_{\mathcal{O}_{f}}$ of $\mathcal{O}_{f}$ by the traces ofthe multipoints of $\rho^{\rm qt}[\mathfrak{M}_{f} ] $ and their conjugates bythe non-trivial element $\varphi\in {\rm Gal}(K/\mathbb{F}_{q}(T))$.

Quantum Drinfeld Modules and Ray Class Fields of Real Quadratic Global Function Fields