Level crossings in complex
two-dimensional potentials
QING-HAI WANG
Department of Physics, National
E-mail: phywq@nus.edu.sg
Abstract. Two-dimensional PT-symmetric quantum-mechanical
systems with the complex cubic
potential $V_{12}=x^2+y^2+igxy^2$ and
the complex H\'enon--Heiles potential $V_{\rm
HH}=x^2+y^2+ig(xy^2-x^3/3)$ are
investigated. Using numerical and
perturbative
methods, energy spectra are obtained to high levels.
Although both potentials respect the PT symmetry, the
complex energy eigenvalues
appear when level crossing happens
between same parity eigenstates.
Keywords. Non-Hermitian;
${\cal PT}$ symmetry; two-dimensional potentials.
PACS Nos 03.65.Ge; 02.30.Lt; 02.60.Lj