Green's function for infinite square well

The Green's function can be given in terms of left and right solutions. $$G(x,x';k) = \frac{1}{W}\left(\Psi_{L}(x_{<})\Psi_{R}(x_{>})\right)$$

But I don't understand how to determine these left and right solutions. These both independently satisfy their own boundary conditions. Can someone explain to me and show the right and left solutions for the infinite square well? Thanks