Non-Hermitian Hamiltonians with real and complex eigenvalues in a   Lie-algebraic framework
  We show that complex Lie algebras (in particular sl(2,C)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians: complexified Scarf II, generalized P\"oschl-Teller, and Morse. The characterizations of these Hamiltonians under the so-called pseudo-Hermiticity are also discussed. 
B. Bagchi, C. Quesne