  Supersymmetric Quantum Mechanics may be used to construct reflectionless
potentials and phase-equivalent potentials. The exactly solvable case of the
$\lambda sech^2$ potential is used to show that for certain values of the
strength $\lambda$ the phase-equivalent singular potential arising from the
elimination of all the boundstates is identical to the original potential
evaluated at a point shifted in the complex cordinate space. This equivalence
has the consequence that certain general relations valid for reflectionless
potentials and phase-equivalent potentials lead to hitherto unknown identities
satisfied by the Associated Legendre functions. This exactly solvable probelm
is used to demonstrate some aspects of scattering theory.
