van Tilburg, Gerrit (2019) Separability and Applications of the Helmholtz Equation. Bachelor's Thesis, Mathematics.
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Abstract
Partial differential equations have different forms for different coordinate systems. In this thesis the separability of two versions of the Helmholtz equation is studied. Conditions on the separability of the scalar Helmholtz equation in n dimensions are given and it is shown that the scalar Helmholtz equation in 3 dimensions separates in 11 coordinate systems. Furthermore, it is found that the vector Helmholtz equation has a more complex form and this equation separates only in rectangular coordinates. Finally, applications of both versions of the Helmholtz equation in quantum mechanics, electromagnetism and optics are treated.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Waalkens, H. and Scholten, O. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 10 Jan 2019 |
| Last Modified: | 16 Jan 2019 11:43 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/18997 |
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