# Relation between Hamiltonian of light ray and that of mechanics

by genxium
Tags: hamiltonian, light, mechanics, relation
 P: 77 I'm learning ray optics and feeling so confused by the definition of "Hamiltonian of light". What I learned was that the "Hamiltonian of light" defined by $H = n-|\vec{p}| = 0$ indicates the momentum conservation, where $n$ is refractive index and $\vec{p}$ here is the canonical momentum. The canonical momentum is defined by $\vec{p}=\frac{dL}{d\vec{r}'}=\frac{dL}{d(\frac{d\vec{r}}{ds})}$ where $\vec{r}$ is the position vector, $s$ is the path length and $L = n*|\vec{r}'|$ is the Lagrangian. My questions are 1. $H$ of light is conserved, but is momentum of light conversed? If so how is it indicated in the equations? 2. $H$ of classical mechanics is $K+V$=kinective energy+potential energy, this is a clear physical meaning, but what does $H$ of light mean? (Sorry for the long definition statement, I wanna make sure that people hold the same definition of things otherwise they can point out where I went wrong)
 Sci Advisor Thanks PF Gold P: 1,908 I don't have an immediate answer for you, but here is a lecture which goes over the same material. Look particularly at p. 34 and following: https://www.fields.utoronto.ca/progr...esJuly2012.pdf
P: 5,510
 Quote by genxium I'm learning ray optics and feeling so confused by the definition of "Hamiltonian of light".

http://en.wikipedia.org/wiki/Hamiltonian_optics

Buchdahl's book is good, too.