matrix in the [$\ell$-SPWA]{}, where $\ell$ is not restricted to belong to a specific symmetry class $$\begin{aligned}
  {\mathbf{K}_{oo,\ell}^{1D,phys}}&=-i\alpha_\ell{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}\quad,\textrm{with}
  \label{eq:kphys_single_pw}
  \\
  \alpha_{\ell}&=\frac{i\Delta_{\ell}}{1-i\Delta_{\ell}{\mathfrak{U}_{\ell\ell}}},
  \label{eq:alpha_ell}\end{aligned}$$ we calculate according to Eqs. and the transmission- and reflection coefficients $$\begin{aligned}
  T^{(\ell)}_{{n{n^{\prime}}}}&=\delta_{{n{n^{\prime}}}}+\frac{\alpha_{\ell}^2\left(2{\operatorname{Tr}[{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}]}({\mathbf{F}_{\ell\ell}^{\mathbf{o}}})_{{n{n^{\prime}}}}\delta_{{n{n^{\prime}}}}-({\mathbf{F}_{\ell\ell}^{\mathbf{o}}})_{{n{n^{\prime}}}}^2\right)}{1-\alpha_{\ell}^2{\operatorname{Tr}[{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}]}^2}\\
  R^{(\ell)}_{{n{n^{\prime}}}}&=\frac{-\alpha_{\ell}^2({\mathbf{F}_{\ell\ell}^{\mathbf{o}}})_{{n{n^{\prime}}}}^2}{1-\alpha_{\ell}^2{\operatorname{Tr}[{\mathbf{F}_{\ell\ell}^{\mathbf{o}}}]}^2},
  \label{eq:tmatrix_closed_form}\end{aligned}$$ from which we derive in particular the total transmission coefficient $T^{(\ell)}_n=\sum_{{n^{\prime}}<n_o}T^{(\ell)}_{{n{n^{\prime}}}}$, when incident in channel $n$ which takes the appealing form $$T_n^{(\ell)}=1-\frac{{\operatorname{Tr}[{\mathbf{K}_{oo,\ell}^{1D,phys}}]}({\mathbf{K}_{oo,\ell}^{1D,phys}})_{nn}}{1+{\operatorname{Tr}[{\mathbf{K}_{oo,\ell}^{1D,phys}}]}^2}
  \label{eq:total_transmission_n}$$ This quantity is in the focus of the following analysis since it encapsulate all the relevant scattering information for both all the open and closed channels.

### General aspects of collisions in harmonic waveguides {#sss:resonance_limits}

In this subsection we focus on the general behavior of the transmission coefficients for partial waves $\ell=0$ and $\ell=1$ at total collision energies beyond the single mode regime. In particular we note, that the separation of length scale induces an energy scale separation. This means that even several quanta of the transversal excitation imply that the corresponding energy dependence of the scaled $s$-wave scattering length is negligible. Due to the increasingly narrow width of higher partial wave resonances, this simplification is not legitimate for $\ell\ge 1$. In addition we should recall that all the scattering lengths used in the analysis below are analytically obtained via 