Non-hermitian Hamiltonians and Painlev\'e IV equation with real   parameters
  In this letter we will use higher-order supersymmetric quantum mechanics to obtain several families of complex solutions of the Painleve IV equation with real parameters. We shall also study the algebraic structure, the eigenfunctions and the energy spectra of the corresponding non-hermitian Hamiltonians. 
David Bermudez and David J. Fernandez C
math-ph hep-th math.MP quant-ph