Browsing by Author "Rajesh Kumar Yadav"

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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 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).
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.
Genetic portrait study for 23 Y-STR loci in the population of Rajasthan, India
(Springer, 2020) Anand Kumar; Rajesh Kumar; R.K. Kumawat; Baiju Mathur; Pankaj Shrivastava; Gyaneshwer Chaubey; Rajesh Kumar Yadav
This study was conducted to come up with data on Y-STR markers for the population of Rajasthan comprising of the western arid region of India. Y-STR analysis is an established tool in forensic DNA casework and ancestry research. We analyzed 23 Y-STRs in randomly selected 310 unrelated individuals living within the geographical area of Rajasthan to establish parameters of forensic interest. Out of 310 haplotypes, 309 unique haplotypes were observed, which revealed a high discrimination capacity with a value of 0.997 for the studied loci. The gene diversity (GD) and haplotype diversity (HD) for the studied 23 Y STRs were found to be 0.664 and 0.666, respectively. In the population of Rajasthan, locus DYS385a/b showed the highest gene diversity with a value of 0.829 among all the studied loci. The studied population showed genetic relatedness with the populations of Madhya Pradesh, Uttar Pradesh, Jharkhand, and Himachal Pradesh. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
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.
Morbidity pattern and their socio-demographic co-relates among rural primary school children in eastern Uttar Pradesh: A cross-sectional study
(Indian Association of Preventive and Social Medicine, 2014) Amit Kaushik; Akash Bansal; Pankaj Kumar Jain; Sandip Kumar; Rajesh Kumar Yadav; Sri Prakash Singh
Research question: What is the morbidity pattern among primary school children in rural area of Varanasi and what their socio-demographic co-relates are? Objective: To study the morbidity pattern among of primary school children in rural Varanasi and to find out various socio-demographic correlates associated with morbidity. Study Design: Descriptive cross sectional study. Setting: Four primary schools from Chiraigaon Community Development Block of Varanasi were selected for study purpose. Participants: Eight hundred and sixteen students from four schools were included in the study by total enumeration of the students present on the day of survey. Results: The present cross-sectional study revealed overall more prevalence of morbidity among female students (86.1%) as compared to their male counterparts (84.4%). Children belonging to scheduled caste, socio-economic status class IV, those whose parents were illiterate and those belonging to joint family had higher prevalence of any morbidity. Caste, socio-economic status, parents' education and type of family were significantly associated with morbidity among school children. Conclusion: Prevalence of morbidities was found to be 2.3 morbidities per child (prevalence) and 2.8 morbidities per sick child. Female students suffered more in comparison to their male counterparts. Nutritional deficiencies were most prevalent. Socio-economic status, caste, literacy of parents and type of family had significant association with morbidity.
Multi-location evaluation of field pea in Indian climates: eco-phenological dynamics, crop-environment relationships, and identification of mega-environments
(Springer Science and Business Media Deutschland GmbH, 2024) Ashok K. Parihar; Kali Krishna Hazra; Amrit Lamichaney; Debjyoti Sen Gupta; Jitendra Kumar; R.K. Mishra; Anil K. Singh; Anuradha Bhartiya; Parvaze Ahmad Sofi; Ajaz A. Lone; Sankar P. Das; Rajesh Kumar Yadav; S.S. Punia; A.K. Singh; Geeta Rai; C.S. Mahto; Khajan Singh; Smita Tiwari; Ashok K. Saxena; Sunil Kumar Nair; Mangla Parikh; Vijay Sharma; Sudhakar P. Mishra; Deepak Singh; Sanjeev Gupta; G.P. Dixit
Characterization of crop-growing environments in relation to crop’s genotypic performance is crucial to harness positive genotype-by-environment interactions (GEI) in systematic breeding programs. Given that, the study aimed to delineate the impact of diverse environments on crop phenology and yield traits of dwarf-statured field pea, pinpointing location(s) favoring higher yield and distinctiveness within breeding lines. We tested twelve field pea breeding lines across twenty locations in India, covering Central Zone (CZ), North Western Plain Zone (NWPZ), North Eastern Plain Zone (NEPZ), and Northern Hill Zone (NHZ). Across these locations, maximum and minimum temperatures during flowering (TMAXF, TMINF) and reproductive period (TMAXRP, TMINRP) ranged 18.9–28.3, 3.3–18.0, 15.0-30.8, and 7.9-22.1oC, respectively. Meanwhile, notable variations in phenological and agronomic traits (coefficient of variation) were observed: flowering (31%), days to maturity (21%), reproductive period (18%), grain yield (48%), and 100-seed weight (18%). Combined ANOVA demonstrated an oversized impact of environment (81%) on yield, while genotype and GEI effects were 2% and 14%, respectively. The variables TMINF, TMINRP, and cumulative growing degree-day showed positive correlations with yield, while extended vegetative and maturity durations negatively influenced yield (p < 0.05). Additionally, linear mixed-models and PCA results explained that instability in crop phenology had significant influence on field pea yield. Seed weight was markedly varied within the locations (9.9–20.8 g) and both higher and lower seed weights were associated with lower yields (Optimal = 17.1 g). HA-GGE biplot-based on environment focus-scaling demonstrated three mega-environments and specific locations viz. Kota (CZ), SK Nagar (CZ), Raipur (CZ), Sehore (CZ), and Pantnagar (NWPZ) as the ideal testing-environments with high efficiency in selecting new genotypes with wider adaptability. The study findings highlight distinct impact of environments on crop phenology and agronomic traits of field pea (dwarf-type), hold substantial value in designing efficient field pea (dwarf-type) breeding program at mega-environment scale. © The Author(s) under exclusive licence to International Society of Biometeorology 2024.
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.
PT phase transition in higher-dimensional quantum systems
(Elsevier B.V., 2013) Bhabani Prasad Mandal; Brijesh Kumar Mourya; Rajesh Kumar Yadav
We consider a 2d anisotropic SHO with ixy interaction and a 3d SHO in an imaginary magnetic field with μ→l.B→ interaction to study the PT phase transition analytically in higher dimension. Unbroken PT symmetry in the first case is complementary to the rotational symmetry of the original Hermitian system. PT phase transition ceases to occur the moment the 2d oscillator becomes isotropic. Transverse magnetic field in the other system introduces the anisotropy in the system and the system undergoes PT phase transition depending on the strength of the magnetic field and frequency of the oscillator. All these results in higher dimensions are based on exact analytical calculations. © 2013 Elsevier B.V. All rights reserved.
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.
The scattering amplitude for a newly found exactly solvable potential
(2013) Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal
The scattering amplitude for a recently discovered exactly solvable shape invariant potential, which is isospectral to the generalized Pöschl-Teller potential, is calculated explicitly by considering the asymptotic behavior of the X1 Jacobi exceptional polynomials associated with this system. © 2013 Elsevier Inc.
The scattering amplitude for one parameter family of shape invariant potentials related to Xm jacobi polynomials
(2013) Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal
We consider the recently discovered, one parameter family of exactly solvable shape invariant potentials which are isospectral to the generalized Pöschl-Teller potential. By explicitly considering the asymptotic behavior of the Xm Jacobi polynomials associated with this system (m=1, 2, 3, ...), the scattering amplitude for the one parameter family of potentials is calculated explicitly. © 2013 Elsevier B.V.
The scattering amplitude for rationally extended shape invariant Eckart potentials
(Elsevier B.V., 2015) Rajesh Kumar Yadav; Avinash Khare; Bhabani Prasad Mandal
We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally extended potentials is calculated analytically for the generalized mth (m=1,2,3,.) case by considering the asymptotic behavior of the scattering state wave functions which are written in terms of some new polynomials related to the Jacobi polynomials. As expected, in the m=0 limit, this scattering amplitude goes over to the scattering amplitude for the conventional Eckart potential. © 2014 Published by Elsevier B.V.