RECONSTRUCTION OF STEP-LIKE POTENTIALS

In this article we study some numerical methods for the determination of a potential V(x) in the one-dimensional Schrodinger equation. We assume that V(x)=0 for x<0, and tends to a nonnegative constant as x tends to positive infinity. We suppose also that there are no bound states. The approach pursued here is a based on a transformation to an equivalent 'time domain' problem, namely the determination of an unknown coefficient in a wave equation. We also discuss some advantages of replacing the unknown potential by an equivalent unknown impedance.