• Level crossings in complex two-dimensional potentials

• # Fulltext

http://www.ias.ac.in/article/fulltext/pram/073/02/0315-0322

• # 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

1. Department of Physics, National University of Singapore, Singapore 117542
• # Pramana – Journal of Physics

Current Issue
Volume 90 | Issue 3
March 2018