particle in the inverse sine-square ($1/\sin^2$) potential. An elegant way to solve the direct problem is to use supersymmetric (SUSY) quantum mechanics with the shape invariance [@Witten; @SUSYQM]. With this, we show that a set of the single-particle eigenstates of the SSD problem can be obtained in closed form for specific values of the parameter $\mu$, which will be introduced in the next section. Then we show that the Slater determinant obtained by filling these single-particle states up to the zero energy is identical to the Slater determinant corresponding to the ground state of the uniform system with PBC. Moreover, we discuss the relation of the SSD in a lattice with that in the continuous space, and clarify the role of the geometric correction involved in the single-particle wavefunctions of the SSD. Then, we demonstrate that a number of properties of the lattice SSD found in the previous study [@Hotta] can be well explained on the basis of the SSD wavefunctions obtained with the use of SUSY quantum mechanics.

The rest of the paper is organized as follows. In section 2, we define the SSD problem of free fermions in 1D continuous space. In section 3, we formulate the single-particle 