Error propagation in the Gel’Fand–Levitan equation

摘要

This paper considers the relationship between errors in momentum measurements and potential energy created through the Gel’Fand–Levitan equation. An assumed error measurement in the reflection coefficient is traced to the associated error in the potential energy. For the case of the error in momentum being proportional to the wave number, it is shown that the potential energy depends on position with the same proportional error; provided that first order approximations hold.