An elementary proof of Rayleigh's principle |
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| Authors: | Kurt Munk Andersen |
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| Affiliation: | 1. Department of Mathematics , Trent Polytechnic, Burton Street , Nottingham NG1 4BU, England;2. Department of Engineering Science , Oxford University, Parks Road , Oxford OX1 3PJ, England |
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| Abstract: | Rayleigh's principle states that the smallest eigenvalue of a regular Sturm-Liouville problem with regular boundary conditions is the minimum value of a certain functional, the so-called Rayleigh quotient, and that this value is attained at the corresponding eigenfunctions only. This can be proved by advanced methods. However, there is an elementary proof, which is presented in this note. |
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