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

Pramana

Zafar Ahmed1¹ 

[1] Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India$$

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

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 𝑥2 and |𝑥| by imaginary $mathcal{PT}$ -symmetric potentials 𝑖𝑥|𝑥| and 𝑖𝑥, respectively.

【 授权许可】

Unknown