Extension of a spectral bounding method to complex rotated Hamiltonians, with application to \(p^2-ix^3\) (Q2774584)

In [J. Phys. A, Math. Gen. 34, No. 19, L271--L277 (2001; Zbl 0979.81036)], \textit{C. R. Handy} presented a novel quantization formalism for generating bounds to the discrete spectra of non-Hermitian potentials. In the paper this formalism is extended to complex rotated transformations of the Hamiltonian \(p^2-ix^3\). Authors solve the non-Hermitian Schrödinger equation NEWLINE\[NEWLINE -\psi''(x)-ix^3\psi(x)=E\psi(x) NEWLINE\]NEWLINE along the complex variable \(x,d\) defined within \(x=e^{i\theta}\xi\), \(-\infty<\xi<\infty\). For this model the moment equation is analysed and some numerical results are given.