Reconstruction of potentials in quantum dots and other small symmetric structures

A method for reconstructing symmetric potentials of Schrödinger operators from a finite set of eigenvalues is presented. The method combines the approach developed by Rundell and Coworkers (SIAM Monographs on Mathematical Modeling and Computation. SIAM: Philadelphia, PA; (1997)) for solving inverse Sturm-Liouville problems with a recent result by Kravchenko (Complex Variables and Elliptic Equations 2008; 53(8):775-789) giving accurate solutions of direct problems. Our construction allows one to recover the potential in situations of great importance in studying nanostructures including quantum dots when only a very limited number of eigenvalues (3-4) obtained experimentally is available.