analytically obtained in section 3.[]{data-label="fig1"}](fig1.eps){width="7cm"}

Before proceeding to the direct comparison of wavefunctions, we discuss the eigenvalue spectrum. Figure \[fig1\] shows the eigenvalue spectrum $\epsilon(m)$ for the lattice SSD problem with $L=101$ and $\mu=0$ in increasing order. In the figure, we also plot the spectrum of the continuous SSD in the negative energy region: $\epsilon (m)= -\kappa\beta(\beta-1)$ with $\beta=50-m$. The overall coefficient $\kappa= 8.2 \times 10^{-4}$ is determined so that the lattice and continuous results are on top of each other. Note that this value of $\kappa$ is clearly consistent with that of the continuous system $ \kappa=(\frac{\pi}{L})^2 \simeq 9.67 \times 10^{-4} $ for $L=101$. As depicted in the figure, we can see that the spectrum of the lattice SSD is well described by that of the continuous SSD in the entire energy range below the Fermi level. This should be contrasted to the fact that the linearization of the single-particle dispersion of the uniform lattice system, which is essential for taking the continuum limit, is valid only in the vicinity of the Fermi level. In this sense, the SSD for the lattice system efficiently smears out the lattice effect.

Using the above correspondence between the lattice and continuous SSD, 