Quantum complex Henon-Heiles potentials

Quantum-mechanical PT-symmetric theories associated with complex cubic pote ntials such as V = x(2) + y(2) + igxy(2) and V = x(2) + y(2) + z(2) + igxyz , where g is a real parameter, are investigated. These theories appear to p ossess real, positive spectra. Low-lying energy levels are calculated to ve ry high order in perturbation theory. The large-order behavior of the pertu rbation coefficients is determined using multidimensional WKB tunneling tec hniques. This approach is also applied to the complex Henon-Heiles potentia l V = x(2) + y(2) + ig(xy(2) - (1/3)x(3)). (C) 2001 Elsevier Science B.V. A ll rights reserved.