• Scarcity of real discrete eigenvalues in non-analytic complex $\mathcal{PT}$-symmetric potentials

• # Fulltext

https://www.ias.ac.in/article/fulltext/pram/073/02/0323-0328

• # Keywords

Non-Hermitian Hamiltonians; real discrete spectrum, $\mathcal{PT}$ symmetry; complex $\mathcal{PT}$-symmetric potentials; Weber function; Airy function.

• # Abstract

We find that a non-differentiability occurring whether in real or imaginary part of a complex $\mathcal{PT}$-symmetric potential causes a scarcity of the real discrete eigenvalues despite the real part alone possessing an infinite spectrum. We demonstrate this by perturbing the real potentials $x^{2}$ and $|x|$ by imaginary $\mathcal{PT}$ -symmetric potentials $ix|x|$ and $ix$, respectively.

• # Author Affiliations

1. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India

• # Pramana – Journal of Physics

Current Issue
Volume 93 | Issue 6
December 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019