  The Parity-Time ($\mathcal{PT}$) symmetric potentials are derived by
non-Hermitian supersymmetric quantum mechanics for square well and barrier.
These $\mathcal{PT}$-supersymmetric square well and barrier. The partners have
complex partners. The partners are isospectral with real energies.
$\mathcal{PT}$-symmetry is only unbroken for the bound states.
