Extension of a spectral bounding method to complex rotated Hamiltonians, with application to p2?-?i?x3

We show that a recently developed method for generating bounds for the discrete energy states of the non-Hermitian -ix3 potential (Handy C R 2001 J. Phys. A: Math. Gen. 34 L271) is applicable to complex rotated versions of the Hamiltonian. This has important implications for extension of the method in the analysis of resonant states, Regge poles, and general bound states in the complex plane (Bender and Boettcher 1998 Phys. Rev. Lett. 80 5243).