On the Sturm–Liouville problem for the complex cubic oscillator

In this paper, solutions of the Sturm–Liouville problem associated with the one‐parameter family of non‐Hermitian Hamiltonians H_α=p²+i(q³+αq) are investigated. We also present some initial results on the distribution of zeros of eigenfunctions. This distribution seems to exhibit a complex version of the classical results on real oscillators.