Open AccessAlternative form of the Gelfand Levitan equation
Author(s) -
Eric Kinca
Publication year - 2021
Publication title -
international journal of applied mathematical research
Language(s) - English
Resource type - Journals
ISSN - 2227-4324
DOI - 10.14419/ijamr.v10i2.31842
Subject(s) - mathematics , structural equation modeling , mathematical analysis , function (biology) , riccati equation , fisher's equation , kernel (algebra) , integro differential equation , partial differential equation , pure mathematics , statistics , evolutionary biology , biology
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.