Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: real spectrum of complex potentials

We propose that the real spectrum and the orthogonality of the states for several known complex potentials of both types, PT-symmetric and non-PT-symmetric, can be understood in terms of currently proposed eta -pseudo-Hermiticity (A. Mostafazadeh, math-ph/0107001) of a Hamiltonian, provided the Hermitian linear automorphism, eta, is introduced as e(-thetap) which affects an imaginary shaft of the coordinate: e-(thetap)xe(thetap) = x + i theta. (C) 2001 Elsevier Science B.V. All rights reserved.