Level crossings in complex two-dimensional potentials

Abstract

Two-dimensional $\mathcal{P}\mathcal{T}$-symmetric quantum-mechanical systems with the complex cubic potential V ₁₂ = x ² + y ² + igxy ² and the complex Hénon-Heiles potential V _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 $\mathcal{P}\mathcal{T}$ symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.