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Inverse Nodal Problems: Finding the Potential from Nodal Lines (Memoirs of the American Mathematical Society)
by Ole H Hald ; Joyce R McLaughlin
Binding: Paperback, 148 pages
Publisher: American Mathematical Society
Weight: 0.65 pound
Dimension: H: 0.25 x L: 10.25 x W: 7 inches
ISBN 10: 0821804863
ISBN 13: 9780821804865
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Book Description:
Can you hear the shape of a drum? No. In this book, the authors ask, 'Can you see the force on a drum?' Hald and McLaughlin prove that for almost all rectangles the potential in a Schr dinger equation is uniquely determined (up to an additive constant) by a subset of the nodal lines. They derive asymptotic expansions for a rich set of eigenvalues and eigenfunctions. Using only the nodal line positions, they establish an approximate formula for the potential and give error bounds. The theory is appropriate for a graduate topics course in analysis with emphasis on inverse problems. Features: The formulas that solve the inverse problem are very simple and easy to state. Nodal Line Patterns Chaldni Patterns are shown to be a rich source of data for the inverse problem. The data in this book is used to establish a simple formula that is the solution of an inverse problem.


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