• Level crossings in complex two-dimensional potentials

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    • Keywords


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

    • Abstract


      Two-dimensional $\mathcal{PT}$-symmetric quantum-mechanical systems with the complex cubic potential 𝑉12 = 𝑥2 + 𝑦2 + 𝑖𝑔𝑥𝑦2 and the complex Hénon–Heiles potential 𝑉HH = 𝑥2 + 𝑦2 + 𝑖𝑔(𝑥𝑦2 − 𝑥3/3) 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.

    • Author Affiliations


      Qing-Hai Wang1

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