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

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      Permanent link:
      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

       

      Zafar Ahmed1

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

       
  • Pramana – Journal of Physics | News

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