Abstract
Quantum-mechanical PT-symmetric theories associated with complex cubic potentials such as V=x2+y2+igxy2 and V=x2+y2+z2+igxyz, where g is a real parameter, are investigated. These theories appear to possess real, positive spectra. Low-lying energy levels are calculated to very high order in perturbation theory. The large-order behavior of the perturbation coefficients is determined using multidimensional WKB tunneling techniques. This approach is also applied to the complex Hénon–Heiles potential V=x2+y2+ig(xy2−(1/3)x3).
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