Title: Inverse Nodal Problems: Finding the Potential from Nodal Lines (Memoirs of the American Mathematical Society)
Publisher: Amer Mathematical Society
Publication Date: 1996
Language: English
ISBN 10: 0821804863
ISBN 13: 9780821804865
Binding: Paperback
Condition: Very Good
Dust Jacket Condition: No Jacket
Weight: 0.51 pounds

About this title

Synopsis

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.

"About this title" may belong to another edition of this title.

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