technique comes at the price of rendering the closed channel $(\hbar \omega_\perp(2n+1)> E)$ components of the wavefunction unphysical. This drawback is due to the boundary conditions of our scattering approach, namely the standing wave approach, which after the analytical continuation to the closed channels turns the oscillating solutions into exponential diverging ones. To overcome this unphysical situation a standard channel closing procedure, familiar from multichannel quantum defect theory has to be applied [@aymar1996], leading to the physical K matrix, given by $${\mathbf{K}_{oo}^{1D,phys}}={\mathbf{K}_{oo}^{1D}}+i {\mathbf{K}_{oc}^{1D}}(1-i{\mathbf{K}_{cc}^{1D}})^{-1}{\mathbf{K}_{co}^{1D}},
  \label{eq:k_oo_1d_phys}$$ where in turn, ${\mathbf{K}_{}^{1D}}$ refers to the corresponding 1D $K$ matrix ${\mathbf{K}_{}^{1D}}=U^{T} {\mathbf{K}^{3D}}U$ [@granger2004; @giannakeas2012; @giannakeas2013; @zhang2013quasi1dscatt]. In addition, ${\mathbf{K}_{oo}^{1D}},{\mathbf{K}_{cc}^{1D}}$ denote the open-open and closed-closed channel transitions, respectively. Accordingly, ${\mathbf{K}_{oc}^{1D}}$ and ${\mathbf{K}_{co}^{1D}}$ denote the open-closed channel transitions and vice versa. From Eq. the resonant processes are given as poles of the physical ${\mathbf{K}_{}^{1D}}$ matrix. Therefore, the roots of $\det(\openone-i{\mathbf{K}_{cc}^{1D}})$ correspond to the positions of the closed channel bound states lying in the continuum of the open channels. The resonant structure thus fulfills a Fano-Feshbach scenario [@chin2010]. Performing the above calculations (cf. Appendix \[app:kphys\]) for a given $3D$ $K$ matrix $K^{3D}=\operatorname{diag}(\tan\delta_{\ell},\tan\delta_{{\ell^{\prime}}})$ yields a physical $K$ matrix, given by $$\begin{aligned}
{\mathbf{K}_{oo}^{1D,phys}}&=\frac{1}{\det(\openone-i
{\mathbf{K}^{3D}}{\mathfrak{U}_{}})}\times\Bigl\{\Delta_\ell{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}+\Delta_{\ell^{\prime}}{\mathbf{F}_{\ell^{\prime}\ell^{\prime}}^{\mathbf{o}}}-\nonumber\\
&-i\Delta_{\ell}\Delta_{\ell^{\prime}}\bigl({\mathfrak{U}_{\ell^{\prime}\ell^{\prime}}}{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}+{\mathfrak{U}_{\ell\ell}}{\mathbf{F}_{\ell^{\prime}\ell^{\prime}}^{\mathbf{o}}}-{\mathfrak{U}_{\ell\ell^{\prime}}}({\mathbf{F}_{\ell\ell^{\prime}}^{\mathbf{o}}}+{\mathbf{F}_{\ell^{\prime}\ell}^{\mathbf{o}}})\bigr)\Bigr\},
\label{eq:kphys}\end{aligned}$$ where $\Delta_{\ell}(E)=\tan\delta_{\ell}(E)$ contains the 