Browsing by Author "Suman Banerjee"

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A class of exactly solvable real and complex PT symmetric reflectionless potentials
(American Institute of Physics Inc., 2024) Suman Banerjee; Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal
We consider the question of the number of exactly solvable complex but PT-invariant reflectionless potentials with N bound states. By carefully considering the Xm rationally extended reflectionless potentials, we argue that the total number of exactly solvable complex PT-invariant reflectionless potentials are 2[(2N − 1)m + N]. © 2024 Author(s).
One parameter family of rationally extended isospectral potentials
(Academic Press Inc., 2022) Rajesh Kumar Yadav; Suman Banerjee; Nisha Kumari; Avinash Khare; Bhabani Prasad Mandal
We start from a given one dimensional rationally extended shape invariant potential associated with Xm exceptional orthogonal polynomials and using the idea of supersymmetry in quantum mechanics, we obtain one continuous parameter (λ) family of rationally extended strictly isospectral potentials. We illustrate this construction by considering three well known rationally extended potentials, two with pure discrete spectrum (the extended radial oscillator and the extended Scarf-I) and one with both the discrete and the continuous spectrum (the extended generalized Pöschl–Teller) and explicitly construct the corresponding one continuous parameter family of rationally extended strictly isospectral potentials. Further, in the special case of λ=0 and −1, we obtain two new exactly solvable rationally extended potentials, namely the rationally extended Pursey and the rationally extended Abraham–Moses potentials respectively. We illustrate the whole procedure by discussing in detail the particular case of the X1 rationally extended one parameter family of potentials including the corresponding Pursey and the Abraham Moses potentials. © 2021 Elsevier Inc.
Solutions of one-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry
(World Scientific, 2023) Suman Banerjee; Rajesh Kumar Yadav; Avinash Khare; Nisha Kumari; Bhabani Prasad Mandal
We consider one-dimensional Dirac equation with rationally extended scalar potentials corresponding to the radial oscillator, the trigonometric Scarf and the hyperbolic Pöschl-Teller potentials and obtain their solution in terms of exceptional orthogonal polynomials. Further, in the case of the trigonometric Scarf and the hyperbolic Pöschl-Teller cases, a new family of Dirac scalar potentials is generated using the idea of parametric symmetry and their solutions are obtained in terms of conventional as well as exceptional orthogonal polynomials. © 2023 World Scientific Publishing Company.