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Inverse Nodal Problems: Finding the Potential from Nodal Lines (Memoirs of the American Mathematical Society)
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ISBN
:
9780821804865
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Publisher
:
Amer Mathematical Society
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Subject
:
Mathematics
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Binding
:
PAPERBACK
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Pages
:
148
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Year
:
1996
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15097.0
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13738.0
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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 SchrxF6;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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