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Recent investigations by Bender and Boettcher (Phys. Rev. Lett 80, 5243(1998)) and Mezincescu (J. Phys. A. 33, 4911 (2000)) have argued that thediscrete spectrum of the non-hermitian potential $V(x) = -ix^3$ should be real.We give further evidence for this through a novel formulation which transformsthe general one dimensional Schrodinger equation (with complex potential) intoa fourth order linear differential equation for $|\Psi(x)|^2$. This permits theapplication of the Eigenvalue Moment Method, developed by Handy, Bessis, andcoworkers (Phys. Rev. Lett. 55, 931 (1985);60, 253 (1988a,b)), yielding rapidlyconverging lower and upper bounds to the low lying discrete state energies. Weadapt this formalism to the pure imaginary cubic potential, generating tightbounds for the first five discrete state energy levels.Comment: Work to appear in J. Phys. A: Math & Ge

Generating converging eigenenergy bounds for the discrete states of the -ix3non-Hermitian potential

Generating converging eigenenergy bounds for the discrete states of the -ix³non-Hermitian potential