About this collection:This is a collection of Lecture Notes on Electromagnetic Theory.An effort is made to keep the content focused on the main topics.There is no discussion of related topics and no digression into unnecessary details.
Who may find it useful:Any one who wants to learn, or refresh all topics, in standard two semester quantum mechanics courses.Topics covered:The list of topics covered appears in the main body of this page. Click on any topic to see details and links to content pages.
These eight lectures on electrodynamics were part of a coursegiven by Pankaj Sharan in Jamia Milia Islamia.
Complete set of 8 lectures can be downloaded from a link below.
We derive the time dependent and time independent Hamilton Jacobi equations, amilton's characetrirstic function is introduced as solution of the time independent equation.
$\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}}$
$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$A canonical transformation is a change of variables \((q,p) \rightarrow (Q,P)\) in phase space such that the Hamiltonian form of equations of motion is preserved. Depending choice of independent variables we have four special cases of canonical transformations., Generating functions for the four cases are introduced and details of the four cases are discussed.
Important relations of four types of transformations are summarized.
Several examples on canonical transformations are given.
The definition finite and infinitesimal canonical transformation are given. Using the action principle we define the generator of a canonical transformation.$\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}}\newcommand{\Label}[1]{\label{#1}}$
$\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}} \newcommand{\PP}[2][]{\frac{\partial^2#1}{\partial #2^2}} \newcommand{\dd}[2][]{\frac{d#1}{d #2}}\newcommand{\DD}[2][]{\frac{d^2#1}{d #2^2}}\newcommand{\Label}[1]{\label{#1}}\newcommand{\eqRef}[1]{\eqref[#1]}$A canonical transformation is a change of variable in phase space such that the equations of motion in the new variables are of the Hamiltonian form.
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