are the creation and the annihilation operators, respectively, of a fermion at site $n$. The lattice spacing is set to unity so that the length of the chain $L$ is the same as the total number of sites. We numerically solve the single-particle problem of ${\hat {\cal H}}_{\rm lat}$ and discuss its relation to the continuous SSD. Let $\chi_m (n)$ be the $m$th single-particle eigenfunction of ${\hat {\cal H}}_{\rm lat}$. The level index $m$ runs from $0$ to $L-1$. The inner product between $\chi_m (n)$ and $\chi_{m'}(n)$ is well-defined and the following orthogonality holds: $\langle \chi_m,\, \chi_{m'} \rangle := \sum^{L}_{n=1} \chi_{m}(n) \chi_{m'}(n) =\delta_{m,m'}$. This suggests that, unlike Eq. (\[innerprod\]), the lattice SSD eigenfunctions do not involve any geometric factor. On the other hand, it is also expected that a naive continuum limit of the lattice SSD eigenfunction $\chi_m (n)$ may approach the eigenfunction of the continuous SSD problem $\psi_\beta^{N-\beta} (x)$. These seemingly contradictory facts can be reconciled by comparing the inner product for the continuous SSD with that for the lattice ones. This leads to the following correspondence: $$\psi_\beta^{N-\beta}(x) \sim \sin \left( \frac{\pi}{L} n \right) \chi_m (n) ,
\label{CLcomparison}$$ with $x\simeq n$, where $\sin ( \frac{\pi}{L} n)$ can be viewed 