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Item Details
| Title:
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INVERSE NODAL PROBLEMS: FINDING THE POTENTIAL FROM NODAL LINES
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| By: |
Ole H. Hald, Joyce R. McLaughlin |
| Format: |
Paperback |
| List price:
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£47.50 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821804863 |
| ISBN 13: |
9780821804865 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
1 January, 1996 |
| Series: |
Memoirs of the American Mathematical Society v. 119 |
| Pages: |
148 |
| Description: |
Can you hear the shape of a drum? In this book, the authors ask, 'Can you see the force on a drum?' It proves that for almost all rectangles the potential in a Schrodinger equation is uniquely determined by a subset of the nodal lines. It presents data that is used to establish a simple formula that is the solution of an inverse problem. |
| Synopsis: |
Can you hear the shape of a drum? 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 Schrodinger 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. 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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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