Inverse nodal problems. Finding the potential from nodal lines.

Hald, Ole H.; McLaughlin, Joyce R.

ISBN 10: 0821804863 / ISBN 13: 9780821804865

Published by Providence, American Math. Soc, 1996

About this Item

Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-00912 9780821804865 Sprache: Englisch Gewicht in Gramm: 150.

Seller Inventory # 2484752

Bibliographic Details

• Title: Inverse nodal problems. Finding the potential from nodal lines.
• Publisher: Providence, American Math. Soc
• Publication Date: 1996
• Language: English
• ISBN 10: 0821804863
• ISBN 13: 9780821804865
• Binding: Softcover
• Weight: 150 grams
• Seller catalogs:
  • SA MATHEMATIK

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 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.