Characteristics of regionally reflectionless potentials - Kincanon, Eric (International Journal of Applied Mathematical Research, 2015)
This paper considers potentials that are reflectionless for a range of energies and not reflectionless elsewhere. The focus of this paper is to see if reflection coefficients of this type have characteristics that would make it possible to solve for the associated potentials using known methods. Using the Gelfand-Levitan equation it is shown that the spectral measure function has several limits that match well to known solved cases. Thus, it seems that pursuing cases of potentials of this type is reasonable.