PT-supersymmetric partner of a short-range square well
  In a box of size $L$, a spatially antisymmetric square-well potential of a purely imaginary strength ${\rm i}g$ and size $l < L$ is interpreted as an initial element of the SUSY hierarchy of solvable Hamiltonians, the energies of which are all real for $g < g_c(l)$. The first partner potential is constructed in closed form and discussed. 
C. Quesne, B. Bagchi, S. Mallik, H. Bila, V. Jakubsky, M. Znojil