Coalescing versus merging of energy levels in one-dimensional potentials

2017/02/27 by Zafar Ahmed, Ahmed, Zafar, Sachin Kumar +5
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1702.08335

openalex publication_date 2017/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The sub-barrier pairs of energy levels of a Hermitian one-dimensional symmetric double well potential are known to merge into one, if the inter-well distance (a) is increased slowly. The energy at which the doublets merge are the ground state eigenvalues of independent wells (ε₀). We show that if the double well is perturbed mildly by a complex PT-symmetric potential the merging of levels turns into the coalescing of two levels at an exceptional point a=a_*. For a>a_*, the real part of complex-conjugate eigenvalues coincides with ε₀ again. This is an interesting and rare connection between the two phenomena in two domains: Hermiticity and complex PT-symmetry.

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