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Non-Hermitian; $\mathcal{PT}$ symmetry; two-dimensional potentials.

Two-dimensional $\mathcal{PT}$-symmetric quantum-mechanical systems with the complex cubic potential $V_{12} = x^{2} + y^{2} + igxy^{2}$ and the complex Hénon–Heiles potential $V_{\text{HH}} = x^{2} + y^{2} + ig(xy^{2} − x^{3}/3)$ are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both potentials respect the $\mathcal{PT}$ symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.

Qing-Hai Wang¹

1. Department of Physics, National University of Singapore, Singapore 117542

Published

August 2009