Bound states for generalized trigonometric and hyperbolic Pöschl–Teller potentials

Alhaidari, A. D.; Assi, I. A.; Mebirouk, A.

doi:10.1142/s0217751x22500129

Cited by 3 publications

(4 citation statements)

References 20 publications

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“…As such, any extension that maintains solvability of (30), leads to a new polar term in the Potential (19), along with a solution of the associated Schrödinger Equation (20). Straightforward examples for such extensions V θ are given by functions that resemble the shape of the trigonometric Pöschl-Teller potential, one of its special cases (as will be shown below), or their generalisations [23]. While the last case is beyond the scope of this article, let us consider a function V θ that has the shape of a trigonometric Pöschl-Teller potential.…”

Section: Extended Trigonometric Pöschl-teller Systemsmentioning

confidence: 99%

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Construction of angular-dependent potentials from trigonometric Pöschl-Teller systems within the Dunkl formalism

Schulze-Halberg

2023

Acta Polytech

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We generate solvable cases of the two angular equations resulting from variable separation in the three-dimensional Dunkl-Schrödinger equation expressed in spherical coordinates. It is shown that the Dunkl formalism interrelates these angular equations with trigonometric Pöschl-Teller systems. Based on this interrelation, we use point transformations and Darboux-Crum transformations to construct new solvable cases of the angular equations. Instead of the stationary energy, we use the constants due to the separation of variables as transformation parameters for our Darboux-Crum transformations.

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Section: Extended Trigonometric Pöschl-teller Systemsmentioning

confidence: 99%

“…Recall that this constant results from applying the reflection operator R 3 , as shown in (24). We can determine r 3 by evaluating (23), taking into account that it only acts on the function Θ. Since we know that: 40) and ( 35) we obtain that:…”

Section: Extended Trigonometric Pöschl-teller Systemsmentioning

confidence: 99%

Construction of angular-dependent potentials from trigonometric Pöschl-Teller systems within the Dunkl formalism

Schulze-Halberg

2023

Acta Polytech

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“…In atomic and molecular physics, the trigonometric Pöschl-Teller potential and its modified form (hyperbolic Pöschl-Teller) are significant potentials and widely used [11,12]. Further generalizing the hyperbolic Pöschl-Teller potential is undoubtedly essential.…”

Section: Introductionmentioning

confidence: 99%

“…Further generalizing the hyperbolic Pöschl-Teller potential is undoubtedly essential. In recent years, many scholars have made extensive studies on the hyperbolic potential from different perspectives [12][13][14]. Although they have studied based on SUSYQM, they only give a form of shape invariance.…”

Section: Introductionmentioning

confidence: 99%

Shape Invariance of Solvable Schrödinger Equations with the Generalized Hyperbolic Pöschl-Teller Potential

Zhong

et al. 2022

Advances in Mathematical Physics

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In atomic and molecular physics, the Pöschl-Teller potential and its modified form (hyperbolic Pöschl-Teller potential) are particularly significant potentials. It is of great importance to study the Schrödinger equation with those potentials. In this paper, we further extend the hyperbolic Pöschl-Teller potential through generalizing the superpotential of that potential of the form Atanh (αx)-Bcoth (αx) to the more general form -Atanh (npx)-Bcoth (mpx). First, we introduce briefly the shape invariance and the potential algebra in supersymmetric quantum mechanics. Second, we derive three additive shape invariances, which are related to parameters A and B of the partner potentials with the generalized superpotential, and discuss the eigenfunctions and eigenvalues in detail. Although the superpotential has two parameters, those shape invariances still belong to the one-parameter form. The reason is that there is always a constraint relationship between A and B in the additive shape invariance of the partner potentials. Third, through the potential algebra approach, we obtain the relevant shape invariance and calculate the corresponding eigenvalue of the Schrödinger equation with the potential of the generalized superpotential. The calculation shows that the algebraic form shape invariance of the partner potentials with that superpotential is anastomotic to the above. Last, we make a summary and outlook.

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Study of the non-relativistic energy spectra of hyperbolic function position dependent mass with Modified Hyperbolic Pöschl Teller potential under AB force

Suparmi,

Maria,

Cari

et al. 2024

12TH INTERNATIONAL SEMINAR ON NEW PARADIGM AND INNOVATION ON NATURAL SCIENCES AND ITS APPLICATIONS (12TH ISNPINSA): Contributio

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Bound states for generalized trigonometric and hyperbolic Pöschl–Teller potentials

Cited by 3 publications

References 20 publications

Construction of angular-dependent potentials from trigonometric Pöschl-Teller systems within the Dunkl formalism

Construction of angular-dependent potentials from trigonometric Pöschl-Teller systems within the Dunkl formalism

Shape Invariance of Solvable Schrödinger Equations with the Generalized Hyperbolic Pöschl-Teller Potential

Study of the non-relativistic energy spectra of hyperbolic function position dependent mass with Modified Hyperbolic Pöschl Teller potential under AB force

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