Theoretical and Natural Science

- The Open Access Proceedings Series for Conferences


Theoretical and Natural Science

Vol. 30, 24 January 2024


Open Access | Article

The Green function approach to scattering amplitude

Yiran Wang * 1
1 Rutgers University

* Author to whom correspondence should be addressed.

Theoretical and Natural Science, Vol. 30, 120-125
Published 24 January 2024. © 2023 The Author(s). Published by EWA Publishing
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citation Yiran Wang. The Green function approach to scattering amplitude. TNS (2024) Vol. 30: 120-125. DOI: 10.54254/2753-8818/30/20241081.

Abstract

Scattering is discussed in classical mechanics, quantum mechanics, and quantum field theory, which shows it is an important part of physics subject. From the Rutherford scattering in classical mechanics to the simple case of a potential barrier impeding the propagating wave in quantum mechanics, scattering problems seem trivial initially but get much more complicated with the study. The scattering theory developed along with the improvement and discovery in physics, and it brings lots of benefits and techniques for researchers from different science fields. To understand the scattering, finding the scattering is a good way to build up the connection between the fundamental theory and intuitive understanding. Specifically, the author wants to emphasize the scattering amplitude in the passage, which repeals the fundamental things of scattering, and the article would include some discussion of the properties of the Green function, which is a powerful mathematical tool for physicists. The author tries to show the scattering amplitude’s beauty through the discussion. Then, link them with the quantum field theory of scattering.

Keywords

Green function, scattering, scattering amplitude, partial wave

References

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3. Thomson, J.J. (1897). Cathode Rays. Philosophical Magazine, 44, 293-316.

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5. Ghosh S, Chandra V. (2020) Scattering cross-section under external magnetic field using the optical theorem. European Physical Journal A, 56:190.

6. Haba Z. (2004). Green functions and propagation of waves in strongly inhomogeneous media. J. Phys. A: Math. Gen. 37, 9295.

7. Martin A. (1959). On the analytic properties of partial wave scattering amplitudes obtained from the Schrödinger equation. Nuovo Cimento, 14(2), 403-425.

8. Sheppard C J R, Kou S S, Lin J. (2014). The Green-function transform and wave propagation. Front. Phys., 2, 00067.

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10. Trivedi, O. (2018). A New Method for Calculating Non Relativistic Feynman Propagators in Momentum Space. arXiv:1811.12288.

Data Availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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Volume Title
Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
ISBN (Print)
978-1-83558-283-1
ISBN (Online)
978-1-83558-284-8
Published Date
24 January 2024
Series
Theoretical and Natural Science
ISSN (Print)
2753-8818
ISSN (Online)
2753-8826
DOI
10.54254/2753-8818/30/20241081
Copyright
24 January 2024
Open Access
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Copyright © 2023 EWA Publishing. Unless Otherwise Stated