DIRAC`S LINEARIZATION APPLIED TO THE FUNCTIONAL, WITH MATRIX ASPECT, FOR THE TIME OF FLIGHT OF LIGHT

Authors : Juan BULNES, José Luıs LÓPEZBONILLA

Pages : 38-43

Doi:10.47087/mjm.1160600

View : 18 | Download : 6

Publication Date : 2022-10-30

Article Type : Research Paper

Abstract :In this paper, we adopt a matrix treatment to solve the variational problem that consists of determining the physical path traveled by light between two points in a medium whose refractive index depends on a spatial coordinate. The considered treatment begins with the trivial repetition of the expression of the value of the considered functional, repetition expressed in the form of a matrix. Next, we adopt the trick insert ignore into journalissuearticles values(of Dirac); originally used as part of the construction of the dynamic equation of relativistic quantum mechanics, which allows us to rewrite the insert ignore into journalissuearticles values(now); matrix integrand in the expression of the value of the functional in terms of the sum of two insert ignore into journalissuearticles values(non-diagonal); matrices brought externally to the problem, which are determined based on some requirements. As a result of this development, we obtain two equivalent versions of Snell`s law.
Keywords : Variational principle in optics, Matrix treatment of a functional and Euler, Dirac