Expression for the Lagrangian for a charged particle in electromagnetic field is given. Gauge invariance of the Lagrangian furnishes an example quasi invariance under the gauge transformations.
$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$
Eliminating cyclic coordinates using Routh's procedure is presented.
Action principle is stated; Euler Lagrange EOM are obtained from the action principle.$\newcommand{\qbf}{\mathbf{q}}$
The equation \[i\hbar\frac{d U(t,t_0)}{dt} = H'_I(t) U(t,t_0).\] obeyed by the time evolution operator in the interaction picture is converted into an integral equation. A perturbative solution is obtained from the integral equation following a standard iterative procedure.
$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
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