Derivation of Jacobian formula with Dirac delta function
- Authors
- Kim, Dohyun; Ee, June-Haak; Yu, Chaehyun; Lee, Jungil
- Issue Date
- 5월-2021
- Publisher
- IOP PUBLISHING LTD
- Keywords
- Jacobian; Dirac delta function; coordinate transformation; chain rule of partial derivatives
- Citation
- EUROPEAN JOURNAL OF PHYSICS, v.42, no.3
- Indexed
- SCIE
SCOPUS
- Journal Title
- EUROPEAN JOURNAL OF PHYSICS
- Volume
- 42
- Number
- 3
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/128100
- DOI
- 10.1088/1361-6404/abdca9
- ISSN
- 0143-0807
- Abstract
- We demonstrate how to make the coordinate transformation or change of variables from Cartesian coordinates to curvilinear coordinates by making use of a convolution of a function with Dirac delta functions whose arguments are determined by the transformation functions between the two coordinate systems. By integrating out an original coordinate with a Dirac delta function, we replace the original coordinate with a new coordinate in a systematic way. A recursive use of Dirac delta functions allows the coordinate transformation successively. After replacing every original coordinate into a new curvilinear coordinate, we find that the resultant Jacobian of the corresponding coordinate transformation is automatically obtained in a completely algebraic way. In order to provide insights on this method, we present a few examples of evaluating the Jacobian explicitly without resort to the known general formula.
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Collections - College of Science > Department of Physics > 1. Journal Articles
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