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Quantum complex Hénon-Heiles potentials. (English) Zbl 0984.81042
Summary: Quantum-mechanical PT-symmetric theories associated with complex cubic potentials 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 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 \(V=x^2+y^2+ig(xy^2-(1/3)x^3)\).

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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