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7 - Eigenfunction rules

Abstract : It is well known that eigenfunctions have to be continuous at each space point of the structure in which they are localized. This is not the only rule they have to fulfill. Rules involving eigenfunction derivatives are also used in the bulk and at the boundary of all physical systems. The aim of this section is to try and reach a general formulation of the eigenfunction rules. At each space point of this network, it is found that the eigenfunctions are continuous and the sum of their outgoing first derivatives is equal to zero. These rules fix the values of the discrete eigenvalues.
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Submitted on : Tuesday, September 28, 2021 - 8:57:17 PM
Last modification on : Tuesday, April 26, 2022 - 4:06:04 PM

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L. Dobrzynski, Housni Al Wahsh, Abdellatif Akjouj, El Houssaine El Boudouti. 7 - Eigenfunction rules. Photonics, Part one: photonic paths, Elsevier, pp.133-145, 2021, 978-0-12-819388-4. ⟨10.1016/B978-0-12-819388-4.00016-2⟩. ⟨hal-03357569⟩

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