Browsing by Author "Nisha Kumari"

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A class of exactly solvable rationally extended Calogero–Wolfes type 3-body problems
(Academic Press Inc., 2017) Nisha Kumari; Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal
In this work, we start from the well known Calogero–Wolfes type 3-body problems on a line and construct the corresponding exactly solvable rationally extended 3-body potentials. In particular, we obtain the corresponding energy eigenvalues and eigenfunctions which are in terms of the product of Xm Laguerre and Xp Jacobi exceptional orthogonal polynomials where both m,p=1,2,3,. © 2017 Elsevier Inc.
A class of exactly solvable rationally extended non-central potentials in two and three dimensions
(American Institute of Physics Inc., 2018) Nisha Kumari; Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal
We start from a seven parameter (six continuous and one discrete) family of non-central exactly solvable potentials in three dimensions and construct a wide class of ten parameters (six continuous and four discrete) family of rationally extended exactly solvable non-central real as well as PT symmetric complex potentials. The energy eigenvalues and the eigenfunctions of these extended non-central potentials are obtained explicitly and it is shown that the wave eigenfunctions of these potentials are either associated with the exceptional orthogonal polynomials or some type of new polynomials which can be further re-expressed in terms of the corresponding classical orthogonal polynomials. Similarly, we also construct a wide class of rationally extended exactly solvable non-central real as well as complex PT-invariant potentials in two dimensions. © 2018 Author(s).
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.
Assessment of gamma and neutron shielding features of Se80-yTe20My (M = Fe, Co, Ni, Cu, y = 0 and 2) alloys for radiation safety applications
(2025) Nisha Kumari; Vishnu Saraswat; Shiv Kumar Pal; Ishu Sharma; Z. Y. Khattari; Neeraj Mehta
[No abstract available]
Group theoretic approach to rationally extended shape invariant potentials
(Academic Press Inc., 2015) Rajesh Kumar Yadav; Nisha Kumari; Avinash Khare; Bhabani Prasad Mandal
The exact bound state spectrum of rationally extended shape invariant real as well as PT symmetric complex potentials is obtained by using potential group approach. The generators of the potential groups are modified by introducing a new operator U(x,J3±12)to express the Hamiltonian corresponding to these extended potentials in terms of Casimir operators. Connection between the potential algebra and the shape invariance is elucidated. © 2015 Elsevier Inc.
Impact of metal doped (Ag, Bi, Cd, Zn) on the structural and optical properties of SeTeSn thin films fabricated via thermal evaporation
(Elsevier Ltd, 2025) Vishnu Saraswat; Nisha Kumari; S.S Salah Fouad; H. Atiya; Neeraj Mehta
This comprehensive research investigates the optical properties of amorphous chalcogenide thin films (TFs) within the multicomponent SeTeSn system doped with Ag, Bi, Cd, and Zn. Key optical parameters critical to applying chalcogenide glasses (ChGs) in optics and optoelectronics have been meticulously evaluated. The optical behaviour of the synthesized TFs was analysed based on experimental reflection and transmission spectra within the 400–2500 nm wavelength range. From the spectral data, we determined critical optical parameters, including the optical band gap (Egopt) and Urbach energy (Ee). Our results indicate that the films exhibit indirect optical transitions, substantiated by the transition power factor (m). We also assessed the real (ε′) and imaginary (ε′′) components of the dielectric constant, uncovering significant changes in dielectric behaviour due to doping. Furthermore, we investigated the dependence of the dissipation factor (tanδ), relaxation time (τ), optical and electrical conductivities, and energy loss functions on photon energy (hv). The nonlinear optical properties were evaluated regarding susceptibility and the nonlinear refractive index, demonstrating the potential of metal-additive Se-Te-Sn glass for optoelectronic applications. Further, A detailed discussion on the potential values of the conduction band (CB) and valence band (VB), along with their respective positions, has also been provided. This research provides a deeper understanding of how metal additive modifies optical and dielectric properties, enhancing the performance of future optoelectronic devices. © 2025 Elsevier B.V.
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.
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.
Rationally extended many-body truncated Calogero–Sutherland model
(Academic Press Inc., 2019) Rajesh Kumar Yadav; Avinash Khare; Nisha Kumari; Bhabani Prasad Mandal
We construct a rational extension of the truncated Calogero–Sutherland model by Pittman et al. The exact solution of this rationally extended model is obtained analytically and it is shown that while the energy eigenvalues remain unchanged, however the eigenfunctions are completely different and written in terms of exceptional X1 Laguerre orthogonal polynomials. The rational model is further extended to a more general Xm case by introducing m dependent interaction term. As expected, in the special case of m = 0, the extended model reduces to the conventional model of Pittman et al. In the two appropriate limits, we thereby obtain rational extensions of the celebrated Calogero–Sutherland as well as Jain–Khare models. The multi-index extension of the model is also discussed. © 2018 Elsevier Inc.
Rationally extended shape invariant potentials in arbitrary d dimensions associated with exceptional Xm polynomials
(Czech Technical University in Prague, 2017) Rajesh Kumar Yadav; Nisha Kumari; Avinash Khare; Bhabani Prasad Mandal
Rationally extended shape invariant potentials in arbitrary D-dimensions are obtained by using point canonical transformation (PCT) method. The bound-state solutions of these exactly solvable potentials can be written in terms of Xm Laguerre or Xm Jacobi exceptional orthogonal polynomials. These potentials are isospectral to their usual counterparts and possess translationally shape invariance property. © Czech Technical University in Prague, 2017.
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.
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.
Tailoring of dielectric behavior and a.c. conduction in binary Se80Te20 glass by incorporation of transition metals (Fe, Co, Ni, Cu)
(Springer, 2024) Nisha Kumari; Vishnu Saraswat; A. Dahshan; Neeraj Mehta
Transition metals (TMs) iron, cobalt, copper, and nickel have been chosen as the chemical modifiers with a binary alloy Se80Te20 as the parent sample to make novel Se78Te20TM2 (TM = Fe, Co, Ni, Cu) alloys. The frequency dependence of dielectric loss and a.c. conductivity (σac) have been studied and the possible mechanism has been checked. The dielectric constant (ε') shows significant variation among the samples, with the parent Se80Te20 alloy exhibiting the highest value, followed closely by Se78Te20Cu2. Conversely, Se78Te20Fe2 and Se78Te20Ni2 alloys exhibit much lower values. The dielectric loss also varies widely, with Se80Te20, while Se78Te20Fe2 and Se78Te20Ni2 alloys present extremely low values of loss. The barrier height ranges between 0.31 eV (Fe-doped sample) and 1.2 eV (Ni-doped sample), indicating that doping influences the band gap significantly. The hooping distance shows considerable differences, with Fe-doped alloys exhibiting the highest value at 39.5 Å, while Co-doped samples show the lowest at 11.4 Å. Applicability of the Meyer-Neldel rule is observed in the a.c. conduction for all samples. The reducing nature of the power-law exponent “s” with increasing temperature indicates the correlated barrier hopping model for Se80Te20 and Se78Te20TM2 (TM = Co, Ni, Cu) alloys, as they exhibit a certain nature of variation. However, because “s” increases with temperature, the non-overlapping small polaron tunneling model is a particularly appropriate mechanism for a.c. conduction of ternary Se78Te20Fe2 alloy. Furthermore, we estimated the density of localized states for the synthesized material at various temperatures. The maximum reduction in the density of states is observed for the iron-containing parent sample. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
Tuning resistive switching behavior and conduction mechanism in Se80Te20 alloy with Fe, Co, Ni, and Cu additives
(Institute of Physics, 2025) Nisha Kumari; Vishnu Saraswat; A. Dahshan; Neeraj Mehta
The present investigations comprehensively analyze the current-voltage characteristics and conduction mechanism in Se80Te20 (ST) and Se78Te20TM2 (STTM; where TM denotes transition metals Cu, Fe, Co, and Ni) glasses. This study focuses on a multi-component system and investigates the voltage-current characteristics of nearly identical disc-shaped specimens at various temperatures below their glass transition points. By analyzing the experimental data, we discovered resistive switching phenomena in both the parent glass and its ternary variants containing transition metals Fe, Co, Ni, and Cu. Remarkably, the resistive switching behavior of these samples has been observed to be related to the Meyer-Neldel rule. Additionally, our findings reveal space charge-limited conduction in binary and ternary alloys. We identified linear relationships between ln I and V1/2 across both low and high voltage ranges, which we explained using the Poole-Frenkel mechanism. While the I-V characteristics showed ohmic behavior at lower voltages, a transition to non-ohmic behavior at higher voltages was attributed to voltage-induced temperature effects. © 2025 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.