PT invariant Non-Hermitian Potentials with Real QES Eigenvalues
  We show that at least the quasi-exactly solvable eigenvalues of the Schr\"odinger equation with the potential $V(x) = -(\zeta \cosh 2x -iM)^2$ as well as the periodic potential $V(x) = (\zeta \cos 2\theta -iM)^2$ are real for the PT-invariant non-Hermitian potentials in case the parameter $M$ is any odd integer. We further show that the norm as well as the weight functions for the corresponding weak orthogonal polynomials are also real. 
Avinash Khare (IOP, Bhubaneswar) and Bhabani Prasad Mandal (SINP,   Calcutta)