REUideaspdf

REUideaspdf - The Method of Trigonometrical Sums in the...

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REU Outline and Ideas I’ve included my ideas and possible approaches to take: 1.Establish the theoretical results of [1] with the Schrodinger Wave Equation. Approach: In a sequential manner, prove the theorems and corollaries associated with the linearly dispersive wave equation in [1] for the Schrodinger Wave equation. Explicitly determine the intervals of time for the fractal and quantized pattern and work out the Fourier series and coef±cients for the same. 2. Study the invariance properties of dispersive wave equations and examine whether it leads to reciprocity relations and important identities related to number-theoretic Weyl Exponential sums. [1] Approach: First, read
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Unformatted text preview: The Method of Trigonometrical Sums in the Theory of Numbers by Vinogradov, I.M and summarize interesting ndings(Ive requested it on Mirlyn). Find number-theoretic results that correlate to the linearly dispersive wave equation and the Schrodinger Wave Equation. Review Quantization of linear maps on a torus Fresnel diffraction by a periodic grating by Hannay, J.H and Berry M.V. to get a better and deeper understanding of the the Greens function and its applicability to Schwartz spaces (we went over this last semester) as well as learning many of the results in greater depth. [1] P.J. Olver. Dispersive quantization. Amer. Math. Monthly, 117:599 610, 2010....
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This note was uploaded on 11/19/2011 for the course MATH 101 taught by Professor Wormer during the Spring '08 term at UCSD.

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