Browsing by Author "Bijan Bagchi"

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A short note on “Group theoretic approach to rationally extended shape invariant potentials” [Ann. Phys. 359 (2015) 46–54]
(Academic Press Inc., 2017) Arturo Ramos; Bijan Bagchi; Avinash Khare; Nisha Kumari; Bhabani Prasad Mandal; Rajesh Kumar Yadav
It is proved the equivalence of the compatibility condition of Ramos (2011, 2012) with a condition found in Yadav et al. (2015). The link of Shape Invariance with the existence of a Potential Algebra is reinforced for the rationally extended Shape Invariant potentials. Some examples on X1 and Xℓ Jacobi and Laguerre cases are given. © 2017 Elsevier Inc.
Generating QES potentials supporting zero energy normalizable states for an extended class of truncated Calogero Sutherland model
(Academic Press Inc., 2024) Satish Yadav; Sudhanshu Shekhar; Bijan Bagchi; Bhabani Prasad Mandal
Motivated by recent interest in the search for generating potentials for which the underlying Schrödinger equation is solvable, we report in the recent work several situations when a zero-energy state becomes bound depending on certain restrictions on the coupling constants that define the potential. In this regard, we present evidence of the existence of regular zero-energy normalizable solutions for a system of quasi-exactly solvable (QES) potentials that correspond to the rationally extended many-body truncated Calogero–Sutherland (TCS) model. Our procedure is based upon the use of the standard potential group approach with an underlying so(2,1) structure that utilizes a point canonical transformation with three distinct types of potentials emerging having the same eigenvalues while their common properties are subjected to the evaluation of the relevant wave functions. These cases are treated individually by suitably restricting the coupling parameters. © 2024 Elsevier Inc.
Parametric symmetries in exactly solvable real and PT symmetric complex potentials
(American Institute of Physics Inc., 2016) Rajesh Kumar Yadav; Avinash Khare; Bijan Bagchi; Nisha Kumari; Bhabani Prasad Mandal
In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex PT symmetric potentials. We focus our attention on the conventional potentials such as the generalized Pöschl Teller (GPT), Scarf-I, and PT symmetric Scarf-II which are invariant under certain parametric transformations. The resulting set of potentials is shown to yield a completely different behavior of the bound state solutions. Further, the supersymmetric partner potentials acquire different forms under such parametric transformations leading to new sets of exactly solvable real and PT symmetric complex potentials. These potentials are also observed to be shape invariant (SI) in nature.We subsequently take up a study of the newly discovered rationally extended SI potentials, corresponding to the above mentioned conventional potentials, whose bound state solutions are associated with the exceptional orthogonal polynomials (EOPs).We discuss the transformations of the corresponding Casimir operator employing the properties of the so(2,1) algebra.
Scattering amplitudes for the rationally extended PT symmetric complex potentials
(Academic Press Inc., 2016) Nisha Kumari; Rajesh Kumar Yadav; Avinash Khare; Bijan Bagchi; Bhabani Prasad Mandal
In this paper, we consider the rational extensions of two different classes of PT symmetric complex potentials namely the asymptotically vanishing Scarf II and asymptotically non-vanishing Rosen–Morse II [ RM-II] and obtain the accompanying bound state eigenfunctions in terms of the exceptional Xm Jacobi polynomials and a certain class of orthogonal polynomials. By considering the asymptotic behavior of the exceptional polynomials, we also derive the reflection and transmission amplitudes for them and discuss the various novel properties of the corresponding amplitudes. © 2016 Elsevier Inc.