Long-range potential scattering: Converting long-range potential to short-range potential by tortoise coordinate Article Swipe
Inspired by general relativity, we suggest an approach for long-range potential scattering. In scattering theory, there is a general theory for short-range potential scattering, but there is no general theory for long-range potential scattering. This is because the scattering boundary conditions for all short-range potentials are the same, but for different long-range potentials, they are different. In this paper, by introducing tortoise coordinates, we convert long-range potential scattering to short-range potential scattering. This allows us to deal with long-range potential scattering as short-range potential scattering. An explicit expression of the scattering wave function for long-range potential scattering is presented, in which the scattering wave function is represented by the tortoise coordinate and the scattering phase shift. We show that the long-range potential scattering wave function is just the short-range potential scattering wave function with a replacement of a common coordinate by a tortoise coordinate. The approach applies not only to scattering but also applies to bound states. Furthermore, in terms of tortoise coordinates, we suggest a classification scheme for potentials. We also discuss the duality between tortoise coordinates.
Related Topics
Concepts
Scattering
Scattering length
Scattering theory
Scattering amplitude
Physics
Mott scattering
Range (aeronautics)
Optical theorem
Quantum mechanics
Small-angle neutron scattering
Neutron scattering
Composite material
Materials science
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1063/5.0024141
- OA Status
- green
- Cited By
- 8
- References
- 56
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4200100462
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4200100462Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1063/5.0024141Digital Object Identifier
- Title
-
Long-range potential scattering: Converting long-range potential to short-range potential by tortoise coordinateWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-12-01Full publication date if available
- Authors
-
Wen-Du Li, Wu-Sheng DaiList of authors in order
- Landing page
-
https://doi.org/10.1063/5.0024141Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/1802.05245Direct OA link when available
- Concepts
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Scattering, Scattering length, Scattering theory, Scattering amplitude, Physics, Mott scattering, Range (aeronautics), Optical theorem, Quantum mechanics, Small-angle neutron scattering, Neutron scattering, Composite material, Materials scienceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
8Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 2, 2024: 1, 2023: 1, 2022: 4Per-year citation counts (last 5 years)
- References (count)
-
56Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| corresponding_institution_ids | https://openalex.org/I162868743 |
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