Level crossings in complex two-dimensional potentials

摘要

Two-dimensional -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 symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.