Alternative form of the Gelfand Levitan equation - Kincanon, Eric (International Journal of Applied Mathematical Research, 2021)
This paper presents an alternative form of the Gelfand-Levitan Equation. By assuming a particular form of the spectral measure function and the potential kernel, an equation relating the potential and the reflection coefficient is found. This equation has an advantage over the Gelfand-Levitan Equation in that it can be solved without using iterative methods. The validity of the equation is demonstrated by looking at a singular and non-singular potential.Â Â