Notices
 

Browse & Filter

For page specific messages
For page author info
Enter a comma separated list of user names.
2651 records found.
Operations
Selected 20 rows in this page.  
Title+Summary Namesort descending Date

[NOTES/QM-17001] Angular Momentum in Quantum Mechanics --- Summary of results

Node id: 4813page

$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$ 
$\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}$
$\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$
$\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$
$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$
$\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
qm-lec-17001

AK-47's picture 22-03-07 19:03:01 y

[NOTES/QCQI-04002] Two Qubit Gates

Node id: 5031page
AK-47's picture 22-04-08 13:04:01 y

[QUE/TH-13004] TH-PROBLEM

Node id: 5175page

The fundamental equation for a system is given by
\begin{equation*}
u = \Lambda \frac{s^{3/2}}{v^{1/2}}
\end{equation*}
where \(\Lambda\) is a constant.
Prove the following equations
\begin{eqnarray}
T &=& \frac{5}{2} \frac{\Lambda S^{3/2}}{NV^{1/2}}\\
P V^{2/3} &=& N \frac{N \Lambda 2^{1/2}}{5*{3/2}} T^{5/3}\\
\mu &=& - \Big(\frac{2}{5}\Big)^{5/2} \frac{2}{\Lambda ^{2/3}} \Big(\frac{V}{N}\Big)^{1/3} T^{5/3}.
\end{eqnarray}

AK-47's picture 22-01-13 17:01:57 n

[2019CM/Final-Part-A]

Node id: 5338page

                                  Classical Mechanics                July 4, 2019   

                                    

 

 Final Examination-PART-A

Instructions

 1  Answers for Part-A to be written on this sheet itself.
2 The answers for PART-B are to be written in a separate answer book.
3 Maximum Time for Part-A is 30 mins.
4  Attempt ALL questions from Part-A.

 

  • Define generalized coordinates. How many generalized coordinates are required for a bead moving on the surface of a sphere? What coordinates will you use?
  • For a particle in three dimensional potential \(\lambda r^4\), write expression of effective potential and plot \(V_\text{eff}(r)\) against \(r\) for non-zero angular momentum.
  • Define canonical transformation in two different ways.
AK-47's picture 22-04-03 11:04:23 n

[2008EM/HMW-10]

Node id: 5407page
AK-47's picture 22-05-10 20:05:39 n

[2003SM/LNP-22] Lecture 22 -- Perfect Fermi Gas

Node id: 5521page
AK-47's picture 22-07-04 10:07:32 n

[1998TH/LNP-17]-

Node id: 5587page
AK-47's picture 22-07-17 18:07:32 n

[NOTES/ME-02009]-Vectors as geometrical objects

Node id: 5669page

Convention about vectors is described. Different different symbols are used for vectors without reference to any axis, components of vector w.r.t. a system of coordinate axes, column vector notation for components

AK-47's picture 22-08-14 10:08:24 n

[NOTES/EM-09004]-Self Inductance and Mutual Inductance

Node id: 5725page

We define the mutual inductance for two loops and self inductance for a loop. We obtain an expression for energy of a circuit with self inductance \(L\)

AK-47's picture 22-08-24 16:08:17 n

[NOTES/QM-09006] Heisenberg Picture of quantum mechanics

Node id: 4709page

The time evolution of states a quantum system is given by the time dependent Schrodinger equation. Besides this framework, called the Schr\"{o}dinger picture, other scheme are possible. In the Heisenberg picture, defined here, the observable evolve according to the equation \[\dd[X]{t} =\frac{1}{i\hbar}[F, H] \]This equation corresponds to the classical equation of motion in the Poisson bracket formalism.


AK-47's picture 24-03-24 18:03:38 n

[NOTES/EM-04002] Poisson Equation in Cylindrical coordinates

Node id: 5972page


Problems with cylindrical symmetry can be solved by separating the variables of the Poisson equation in cylindrical coordinates.  The separation of variables for this class of problems and boundary conditions are explained.

AK-47's picture 23-10-25 06:10:18 n

[NOTES/QM-25001] Electormagnetic Waves

Node id: 4928page

$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$ 
$\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}$
$\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$
$\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$
$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$
$\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
$\newcommand{\ket}[1]{\langle #1\rangle}$
qm-lec-25001

AK-47's picture 22-03-12 18:03:06 y

[QUE/EM-02023] EM-PROBLEM

Node id: 5126page

Use Gauss's law to find the electric field inside a uniformly charged
solid sphere of radius \(R\) and carrying charged density $\rho$. State facts
other than Gauss's law which you might have used in your answer.

AK-47's picture 22-01-09 21:01:52 n

[QUE/TH-06011] TH-PROBLEM

Node id: 5206page

(a) Show that the work done on an ideal gas to compress it
isothermally is greater than that necessary to compress it
adiabatically if the pressure change is the same in two
processes.
(b)~Show that the isothermal work is less than the adiabatic work if
the volume change is the some in two processes
(c)~As numerical example, compare the work done from initial
pressure and volume to be 10$^6$N/m$^2$ 0.5 m$^3$ kilomole$^{-}$ in
the isothermal and adiabatic process when
(i)~the pressure is doubled (ii)~ volume is halved.

AK-47's picture 22-01-20 15:01:42 n

[2019EM/HMW-06]

Node id: 5368page

Electrodynamics                                                                          Oct 17, 2018
                                                Tutorial-V (VI)

  • A cylindrical resistor of length \(\ell\), radius \(a\) and resistivity $\varrho$ carrying a current \(i\).
    1. Show that the Poynting vector $\vec{S}$ at the surface of the resistor is everywhere directed to the normal to the surface, as shown,
    2. Show the rate $\rho$ at which energy flows into the resistor through its cylindrical surface, calculated by integrating the Poynting vector over this surface, is equal to the rate at which Joule heat is produced, i.e. \begin{equation*} \int\vec{S}\cdot\vec{dA}=i^2R \end{equation*}
  • Figure 1 shows a parallel-plate capacitor being charged,
    1. Show that the Poynting vector \(S\) points everywhere radially into the cylindrical volume.
    2. Show that the rate \(P\) at which energy flows into this volume, calculated by integrating the Poynting vector over the cylindrical boundary of this volume, is equal to the rate at which the stored electrostatic energy increases; that is, that \[\int \vec{S}\cdot\vec{dA} = A d \frac{1}{2}\frac{d}{dt}(\epsilon \vec{E}^2)\],where \(Ad\) is the volume of the capacitor and \(\frac{1}{2} \epsilon_0\vec{E}^2\) is the energy density for all points within that volume. This analysis shows that, according to the Poynting vector point of view, the energy stored in a capacitor does not enter it through the wires but through the space around the wires and the plates. \{Hint: To find \(S\) we must first find \(B\), which is the magnetic field setup by the displacement current during the charging process; Ignore fringing of the lines of \(E\).)\}
  • A coaxial cable (inner radius \(a\) and outer radius \(b\)) is used as a transmission line between a battery $\epsilon$ and a resistor \(R\),
  1. [(a)] Calculate $\vec{E}, \vec{B}$ for $a < r < b$
  2. [(b)] Calculate Poynting vector S for $a< r < b.$
  3. [(c)] By suitably integrating the Poynting vector, Show that the total power flowing across the annular cross section $a<r<b$ is="" $\epsilon^{2}="" r$.="" this="" reasonable="" ?="" <="" li="">
  4. [(d)] Show that the direction of $\vec{S}$ is always away from the battery to resistor, no matter which way is the battery connected.

 

AK-47's picture 22-04-25 19:04:10 n

[QUE/EM-02001]

Node id: 5439page

[1] A thin glass rod is bent into a semicircle of radius $R$. A charge $+Q$ is
uniformly distributed along the upper half and a charge $-Q$ is distributed
uniformly along the lower half as shown in the figure. Find the electric field
at
P, the center of the semicircle.

AK-47's picture 22-05-24 13:05:33 n

[1998TH/LNP-09] Lecture -9 Equation of State-II

Node id: 5551page
AK-47's picture 22-07-08 07:07:29 n

[RCQ/CV-05002] Recalling Reasoning for Singular Points

Node id: 5627page
AK-47's picture 22-08-06 19:08:16 n

[NOTES/ME-14005]-Vectors and Tensors

Node id: 5699page
AK-47's picture 22-08-16 16:08:18 n

[NOTES/EM-12001]-Lorentz transformations

Node id: 5757page

The basic equations of Maxwell's theory are written down in relativistic notation. Using Lorentz transformations of the potentials, the expressions of the scalar and vector potentials of a point charge moving with a uniform velocity are obtained.


 

AK-47's picture 23-03-03 21:03:55 n

Pages

 
X