A Class of Exactly Solvable Real and Complex $PT$ Symmetric Reflectionless Potentials

Suman Banerjee; Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal

A Class of Exactly Solvable Real and Complex $PT$ Symmetric Reflectionless Potentials

Quantum Physics 2023-09-11 v1 High Energy Physics - Theory Mathematical Physics Dynamical Systems math.MP

Authors: Suman Banerjee , Rajesh Kumar Yadav , Avinash Khare , Bhabani Prasad Mandal

Abstract

We consider the question of the number of exactly solvable complex but PT-invariant reflectionless potentials with $N$ bound states. By carefully considering the $X_m$ rationally extended reflectionless potentials, we argue that the total number of exactly solvable complex PT-invariant reflectionless potentials are $2[(2N-1)m+N]$ .

Keywords

painlevé equations and orthogonal polynomials

Cite

@article{arxiv.2308.05917,
  title  = {A Class of Exactly Solvable Real and Complex $PT$ Symmetric Reflectionless Potentials},
  author = {Suman Banerjee and Rajesh Kumar Yadav and Avinash Khare and Bhabani Prasad Mandal},
  journal= {arXiv preprint arXiv:2308.05917},
  year   = {2023}
}

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26 pages, 49 figures

A Class of Exactly Solvable Real and Complex $PT$ Symmetric Reflectionless Potentials

Abstract

Keywords

Cite

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