Publisher's 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 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.
