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Title	Name	Date
[NOTES/EM-03005] Charged Particle In Electromagnetic Field 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. $\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$	kapoor	24-03-26 22:03:15
[NOTES/QM-09008] Perturbation Expansion in Interaction picture 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. $\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1\|#2\|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\average}[2]{\langle#1\|#2\|#1\rangle}$	AK-47	24-03-24 19:03:37
[NOTES/QM-09004] Stationary States and Constants of Motion $\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1\|#2\|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\average}[2]{\langle#1\|#2\|#1\rangle}$ The eigenstates of Hamiltonian are called stationary states.In a stationary state all observable quantities are independent of time. The dynamical variables which commute with Hamiltonian are called constants of motion. The average values of constants of motion in any state do not change with time.	AK-47	24-03-24 19:03:48
[NOTES/QM-09007] Interaction Picture of Quantum Mechanics $\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1\|#2\|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}\newcommand{\average}[2]{\langle#1\|#2\|#1\rangle}$ The interaction picture, also known as Dirac picture, or the intermediate picture, is defined by splitting the Hamiltonian in two parts, the free and the interaction parts. In interaction picture equation of motion for the observables is free particle equation. The state vector satisfies Schrodinger equation with interaction Hamiltonian giving the rate of time evolution.	AK-47	24-03-24 19:03:00
[NOTES/QM-09003] Solution of TIme Dependent Schrodinger Equation $\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$ $\newcommand{\matrixelement}[3]{\langle#1\|#2\|#3\rangle}$ $\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$ $\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$ $\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$ A scheme to solve the time dependent Schr\"{o}dinger equation \begin{equation} \label{eq01} i\hbar \dd{t}\ket{\psi} = \hat{H} \ket{\psi} \end{equation} is described. The final solution will be presented in the form, see \eqref{eq14} \begin{equation} \ket{\psi t} = U(t, t_0) \ket{\psi t_0} \label{eq16} \end{equation}where \begin{equation}\label{EQ16A} U(t, t_0) \ket{\psi t_0} = \exp\Big(\frac{-i H(t-t_0)}{\hbar}\Big)\end{equation}	AK-47	24-03-23 05:03:26
[NOTES/SM-01001] Thermodynamic Coodinates	kapoor	24-03-20 15:03:27
[NOTES/CM-02003] From Newton's EOM to Euler Lagrange EOM Euler Lagrange equations are obtained using Newton's laws and D' Alembert's principle. $\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$	kapoor	24-03-15 06:03:32
[NOTES/CM-02001] Limitations of Newtonian Mechanics Some limitations of Newtonian mechanics are pointed out.	kapoor	24-03-15 04:03:24
[NOTES/QFT-01001] Examples of Classical Fields After recalling the analytical dynamics briefly, several examples of systems with infinite degrees of freed are given.	kapoor	24-03-10 09:03:01
[NOTES/EM-07013] Conservtion of Electromagnetic Field Momentum.* The equation of continuity appears in different branches of physics. It represents a local conservation law. In order to be consistent with requirement if special relativity every conserved quantity must come with a current which gives the flow of the conserved quantity across a surface and the two must obey equation of continuity. Taking the example of momentum conservation, we briefly discuss the interpretation of stress tensor giving flow of momentum per unit time as a surface integral. The surface integral, in turn, gives the force on the surface. $\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\dd}[2][]{\frac{d#1}{d#2}}$	kapoor	24-03-02 11:03:19

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