Browsing by Author "Satish Yadav"

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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.
Osteopetrosis in two siblings: Two case reports Genetics
(BioMed Central Ltd., 2016) Satish Yadav; Shiv Chalise; Shipra Chaudhary; Gauri Shankar Shah; Mukesh Kumar Gupta; Om Prakash Mishra
Background: Osteopetrosis is a rare inherited metabolic bone disorder characterized by extensive sclerosis of skeletons, visual and hearing impairment, hepatosplenomegaly and anemia. It has two major clinical forms: the autosomal dominant adult (benign) form is associated with milder symptoms often appearing in later childhood and adulthood whereas the autosomal recessive infantile (malignant) form has severe presentations appearing in very early childhood, if untreated, is typically fatal during infancy or early childhood. A rare autosomal recessive (intermediate) form is present during childhood with some signs and symptoms of malignant osteopetrosis. Diagnosis is mainly based on clinical and typical generalized increase in bone density. Case presentation: The two siblings of Indo-Aryan ethnicity, aged five and 8 years, were admitted with irregular low grade fever and gradually increasing abdominal mass for last 3 years. They also had history of hearing loss. On examination, the patients were found pale with poor nutritional status, short stature, frontal bossing and splenomegaly. We made a clinical diagnosis of hemolytic anemia and investigated accordingly. Peripheral Blood Smear was suggestive of leucoerythroblastic picture in both the siblings. We extended our investigations and radiological survey revealed generalized increase in bone density which was consistent with osteopetrosis. Conclusion: Osteopetrosis is a rare disease transmitted by autosomal dominant or recessive inheritance having variable penetrance. We report here milder form of disease in the two siblings having typical clinical features in the form of anemia, hepatosplenomegaly and hearing loss. Diagnosis was confirmed by typical generalized increase in bone density in both the patients. © 2016 Yadav et al.
Solving New Potentials in Terms of Exceptional Orthogonal Polynomials and Their Supersymmetric Partners
(Springer, 2025) Satish Yadav; Rahul Ghosh; Bhabani Prasad Mandal
Point canonical transformation has been used to find out new exactly solvable potentials in the position-dependent mass framework. We solve 1-D Schrödinger equation in this framework by considering two different fairly generic position-dependent masses (i)M(x)=λg′(x) and (ii)M(x)=cg′(x)ν, ν=2η2η+1, with η=0,1,2⋯. In the first case, we find new exactly solvable potentials that depend on an integer parameter m, and the corresponding solutions are written in terms of Xm-Laguerre polynomials. In the latter case, we obtain a new one parameter (ν) family of isochronous solvable potentials whose bound states are written in terms of Xm-Laguerre polynomials. Further, we show that the new potentials are shape invariant by using the supersymmetric approach in the framework of position-dependent mass. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
Supersymmetry and shape invariance of exceptional orthogonal polynomials
(Academic Press Inc., 2022) Satish Yadav; Avinash Khare; Bhabani Prasad Mandal
We discuss the exceptional Laguerre and the exceptional Jacobi orthogonal polynomials in the framework of the supersymmetric quantum mechanics (SUSYQM). We express the differential equations for the Jacobi and the Laguerre exceptional orthogonal polynomials (EOP) as the eigenvalue equations and make an analogy with the time independent Schrödinger equation to define “Hamiltonians” enables us to study the EOPs in the framework of the SUSYQM and to realize the underlying shape invariance associated with such systems. We show that the underlying shape invariance symmetry is responsible for the solubility of the differential equations associated with these polynomials. © 2022 Elsevier Inc.