Inverse Nodal Problems: Finding the Potential from Nodal Lines (Memoirs of the American Mathematical Society) - Softcover

Hald, Ole H.; McLaughlin, Joyce R.

 
9780821804865: Inverse Nodal Problems: Finding the Potential from Nodal Lines (Memoirs of the American Mathematical Society)
Softcover
ISBN 10: 0821804863 ISBN 13: 9780821804865
Publisher: Amer Mathematical Society, 1996

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 Schrödinger 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.

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

Publisher
Amer Mathematical Society
Publication date
1996
Language
English
ISBN 10 
0821804863
ISBN 13 
9780821804865
Binding
Paperback
Number of pages
148