Group theoretic approach to rationally extended shape invariant potentials

Yadav, Rajesh K.; Kumari, Niraj; Khare, Avinash; Mandal, Bhabani Prasad

doi:10.1016/j.aop.2015.04.002

Cited by 21 publications

(20 citation statements)

References 45 publications

(50 reference statements)

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“…which is nothing butW i (r) given in (17). In addition, substituting W i (x) = −W i (x) in (42) gives (16), with R 1 = E m .…”

Section: Qhjf and The Isospectral Deformationmentioning

confidence: 99%

“…The explicit expressions for P αi m (r) obtained by substituting different W i (r) in (16) along with the condition on R 1 are also given. These in turn give differentW i (r) from (17). In addition the explicit expressions for the three families of the rational potentialsṼ − i (r), obtained using (20), are given in table 3, along with their solutions, constructed using (23) and (25).…”

Section: First Iteration Of Isospectral Deformation Of the Radial Oscmentioning

confidence: 99%

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Quantum Hamilton–Jacobi route to exceptional Laguerre polynomials and the corresponding rational potentials

Ranjani

2019

Pramana - J Phys

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A method to construct multi-indexed exceptional Laguerre polynomials using isospectral deformation technique and quantum Hamilton-Jacobi (QHJ) formalism is presented. We construct generalized superpotentials using singularity structure analysis which lead to rational potentials with multi-indexed polynomials as solutions. We explicitly construct such rational extensions of the radial oscillator and their solutions, which involve exceptional Laguerre orthogonal polynomials having two indices. The exact expressions for the L1, L2 and L3 type polynomials, along with their weight functions are presented. We also discuss the possibility of constructing more rational potentials with interesting solutions.keywords Exceptional orthogonal polynomials, multi-indexed exceptional polynomials, exactly solvable models, rational potentials, shape invariance, isospectral deformation, quantum Hamilton-Jacobi formalism, quantum momentum function. 1

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“…which is nothing butW i (r) given in (17). In addition, substituting W i (x) = −W i (x) in (42) gives (16), with R 1 = E m .…”

Section: Qhjf and The Isospectral Deformationmentioning

confidence: 99%

Section: First Iteration Of Isospectral Deformation Of the Radial Oscmentioning

confidence: 99%

Quantum Hamilton–Jacobi route to exceptional Laguerre polynomials and the corresponding rational potentials

Ranjani

2019

Pramana - J Phys

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“…In most of these cases, these new potentials are the rational extension of the corresponding conventional potentials [15,16]. Various properties of these new extended potentials have also been studied by different groups [17,18,19,20,21,22,23,24,25,26]. It is then natural to consider the rational extension of the conventional non-central potentials discussed in Ref.…”

Section: Introductionmentioning

confidence: 99%

A class of exactly solvable rationally extended non-central potentials in two and three dimensions

Kumari

Yadav

Khare

et al. 2018

Journal of Mathematical Physics

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We start from a seven parameters (six continuous and one discrete) family of non-central exactly solvable potential 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 P T 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 (EOPs) 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.

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“…Apart from that, in [31] it has been considered the complex Lie algebra sl(2, C) when dealing with non-Hermitian Hamiltonians with real eigenvalues. Later on, in [32] a group theoretical approach to some extended Shape Invariant potentials has been developed, in which another condition has to be satisfied by the seed superpotential and the functions defining the extension. This technique was further employed by Yadav et al in [33].…”

Section: Introductionmentioning

confidence: 99%

A short note on “Group theoretic approach to rationally extended shape invariant potentials” [Ann. Phys. 359 (2015) 46–54]

et al. 2017

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It is proved the equivalence of the compatibility condition of [A. Ramos, J. Phys. A 44 (2011) 342001, Phys. Lett. A 376 (2012) 3499] with a condition found in [Yadav et al., Ann. Phys. 359 (2015) 46]. The link of Shape Invariance with the existence of a Potential Algebra is reinforced for the rationally extended Shape Invariant potentials. Some examples on X 1 and X ℓ Jacobi and Laguerre cases are given.

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Group theoretic approach to rationally extended shape invariant potentials

Cited by 21 publications

References 45 publications

Quantum Hamilton–Jacobi route to exceptional Laguerre polynomials and the corresponding rational potentials

Quantum Hamilton–Jacobi route to exceptional Laguerre polynomials and the corresponding rational potentials

A class of exactly solvable rationally extended non-central potentials in two and three dimensions

A short note on “Group theoretic approach to rationally extended shape invariant potentials” [Ann. Phys. 359 (2015) 46–54]

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