Scattering by a collection of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si2.svg"><mml:mi>δ</mml:mi></mml:math>-function point and parallel line defects in two dimensions

Bui, Hai Viet; Loran, Farhang; Mostafazadeh, Alí

doi:10.1016/j.aop.2021.168649

Cited by 2 publications

(2 citation statements)

References 31 publications

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“…In this case, we need to choose the coupling constants or strengths as functions of regularization parameter such that the limit converges. For an alternative treatment of scattering applied to coexisting point and line defects see the recent work [20].…”

Section: Introductionmentioning

confidence: 99%

Delta Potentials Supported by Hybrid Geometries and Their Deformations

Erman¹,

Seymen²,

Turgut³

2022

Preprint

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We study the hybrid type of delta potentials in R 2 and R 3 , where the delta potentials supported by a circle/sphere are considered together with the delta potentials supported by a point outside of the circle/sphere. The construction of the self-adjoint Hamiltonian operator associated with the formal Hamiltonian operator for the circle and point delta potentials is explicitly given. The bound state energies and scattering properties for each problem are also studied. Finally, we consider the delta potentials supported by deformed circle/sphere and show that first order change in the bound state energies under the small deformations of circle/sphere is equal to the first order perturbative solution of the bound state energy calculated from the delta potential whose support is increased by the average of the deformation over the circle/sphere.

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Section: Introductionmentioning

confidence: 99%

Delta Potentials Supported by Hybrid Geometries and Their Deformations

Erman¹,

Seymen²,

Turgut³

2022

Preprint

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show abstract

“…For an alternative treatment of scattering applied to the co-existing point and line defects, see also the recent work. 28 )…”

Section: Introductionmentioning

confidence: 99%

Rank one perturbations supported by hybrid geometries and their deformations

Erman

Seymen

Turgut

2022

Journal of Mathematical Physics

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We study the hybrid type of rank one perturbations in [Formula: see text] and [Formula: see text], where the perturbation supported by a circle/sphere is considered together with the delta potential supported by a point outside of the circle/sphere. The construction of a self-adjoint Hamiltonian operator associated with formal expressions for the rank one perturbation supported by a circle and by a point is explicitly given. Bound state energies and scattering properties for each problem are also studied. Finally, we consider the rank one perturbation supported by a deformed circle/sphere and show that the first order change in bound state energies under small deformations of the circle/sphere has a simple geometric interpretation.

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Scattering by a collection of δ-function point and parallel line defects in two dimensions

Cited by 2 publications

References 31 publications

Delta Potentials Supported by Hybrid Geometries and Their Deformations

Delta Potentials Supported by Hybrid Geometries and Their Deformations

Rank one perturbations supported by hybrid geometries and their deformations

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