Deformed Morse-like potential

Assi, I. A.; Alhaidari, A. D.; Bahlouli, H.

doi:10.1063/5.0046346

Cited by 6 publications

(3 citation statements)

References 24 publications

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“…It should be noted that the observations made above about the sign of the potential parameter C are consistent with the SPDs shown in the figure . A detailed description of the SPD, its benefits, and how to construct it are found in Ref. [7]. In the atomic units…”

Section: Introductionmentioning

confidence: 99%

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Finite-Series Approximation of the Bound States for Two Novel Potentials

Alhaidari

Assi

2022

Physics

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We obtain an analytic approximation of the bound states solution of the Schrödinger equation on the semi-infinite real line for two potential models with a rich structure as shown by their spectral phase diagrams. These potentials do not belong to the class of exactly solvable problems. The solutions are finite series (with a small number of terms) of square integrable functions written in terms of Romanovski–Jacobi polynomials.

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Section: Introductionmentioning

confidence: 99%

“…, where h is the Planck's constant and m is the mass, the time-independent Schrödinger equation in the configuration space x for the potential ( ) V x and energy E is as follows: A detailed description of the SPD, its benefits, and how to construct it are found in Ref. [7]. In the atomic units…”

Section: Introductionmentioning

confidence: 99%

Finite-Series Approximation of the Bound States for Two Novel Potentials

Alhaidari

Assi

2022

Physics

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“…Recently the entropy-and complexity-like properties of these polynomials, which determine their spreading on the orthogonality interval, have begun to be investigated by means of the entropy-and complexity-like measures [11,48,49] of the associated Rakhmanov density ρ n (x) = p 2 n (x) h(x). This normalized-to-unity probability density function governs the (n → +∞)-asymptotics of the ratio of two polynomials with consecutive orders [57], and characterizes the Born's probability density of the bound stationary states of a great deal of quantum-mechanical potentials which model numerous atomic and molecular systems [12,14,41,[50][51][52]. The numerical evaluation of the integral functionals corresponding to the dispersion, entropic and complexity measures of the HOPs by means of the standard quadratures is not convenient, because the highly oscillatory nature of the integrand renders Gaussian quadrature ineffective as the number of quadrature points grows linearly with n and the evaluation of high-degree polynomials are subject to round-off errors.…”

Section: Introductionmentioning

confidence: 99%

Algebraic $\mathcal{L}_{q}$-norms and complexity-like properties of Jacobi polynomials-Degree and parameter asymptotics

Sobrino¹,

Dehesa²

2021

Preprint

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The Jacobi polynomials P (α,β) n (x) conform the canonical family of hypergeometric orthogonal polynomials (HOPs) with the two-parameter weight functionThe spreading of its associated probability density (i.e., the Rakhmanov density) over the orthogonality support has been quantified, beyond the dispersion measures (moments around the origin, variance), by the algebraic Lq-norms (Shannon and Rényi entropies) and the monotonic complexity-like measures of Cramér-Rao, Fisher-Shannon and LMC (López-Ruiz, Mancini and Calbet) types. These quantities, however, have been often determined in an analytically highbrow, non-handy way; specially when the degree or the parameters (α, β) are large. In this work, we determine in a simple, compact form the entropic and complexity-like properties of the Jacobi polynomials in the two extremal situations: (n → ∞; fixed α, β) and (α → ∞; fixed n, β). These two asymptotics are relevant per se and because they control the physical entropy and complexity measures of the high energy (Rydberg) and high dimensional (pseudoclassical) states of numerous supersymmetric quantum-mechanical systems.

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Algebraic and complexity‐like properties of Jacobi polynomials: Degree and parameter asymptotics

Sobrino

Dehesa

2021

Int J of Quantum Chemistry

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The Jacobi polynomials Pfalse^nαβ()x conform the canonical family of hypergeometric orthogonal polynomials (HOPs) with the two‐parameter weight function 1−xα1+xβ,α,β>−1, on the interval [],−1+1. The spreading of its associated probability density (i.e., the Rakhmanov density) over the support interval has been quantified, beyond the dispersion measures (moments around the origin, variance), by the algebraic Lq‐norms (Shannon and Rényi entropies) and the monotonic complexity‐like measures of Cramér–Rao, Fisher–Shannon, and LMC (López‐Ruiz, Mancini, and Calbet) types. These quantities, however, have been often determined in an analytically highbrow, non‐handy way; specially when the degree or the parameters (),αβ are large. In this work, we determine in a simple, compact form the leading term of the entropic and complexity‐like properties of the Jacobi polynomials in the two extreme situations: (n→∞; fixed α,β) and (α→∞; fixed n,β). These two asymptotics are relevant per se and because they control the physical entropy and complexity measures of the high energy (Rydberg) and high dimensional (pseudoclassical) states of many exactly, conditional exactly, and quasi‐exactly solvable quantum‐ mechanical potentials which model numerous atomic and molecular systems.

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Deformed Morse-like potential

Cited by 6 publications

References 24 publications

Finite-Series Approximation of the Bound States for Two Novel Potentials

Finite-Series Approximation of the Bound States for Two Novel Potentials

Algebraic $\mathcal{L}_{q}$-norms and complexity-like properties of Jacobi polynomials-Degree and parameter asymptotics

Algebraic and complexity‐like properties of Jacobi polynomials: Degree and parameter asymptotics

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