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### Resources Contributed by Prof. H. S. Mani-Home-Page

Node id: 5270collection

22-02-25 20:02:59 n

### Stockpile :: Complex Variables --- Problem Solving Sessions

Node id: 3533collection

• There is one stockpile for each area of Physics and of Mathematical Physics
• The stockpiles of resources for teaching and learning, and problem solving.
• Items available under Lessons, Problem Solving and Evaluation and Assessment are designed as stand alone,  independent resources.
• Stockpile are useful for those who have some exposure to the subject. Recommended for students attending a course and for teachers.
• Choose a topic and start learning, or start solving problems.
• Each module will cover all aspects of teaching and learning for a set of a small number of closely related topics.
• The Newbies will find Self Paced Courses more useful.

22-08-01 11:08:38 n

### SUNDAY-PHYSICS October 3, 2022 Lecture 12

Node id: 5780page
22-10-03 04:10:30 n

### The structure of physical theories

Node id: 4630page
21-09-07 09:09:06 n

### Time Evolution of Quantum systems : A Summary

Node id: 4712page

$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
$\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}$
$\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$
$\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$
$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$
$\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
qm-lec-09009

21-09-28 20:09:44 y

### Unit-A Vectors, Summation Convention [LNK}

Node id: 3396page
22-08-26 00:08:17 n

### View Assignments and Solutions On Line

Node id: 2458page

This is a collection of assignments and examination papers of a course in
"Elementary Particle Physics" given by Professor H.S. Mani
at University of Hyderabad in the year 2009.

21-08-22 02:08:59 n

### Works of Masters always have something to offer

Node id: 723page

I take the best from every one. But GOLD FROM OLD,
There is always something to learn from  MASTERS;

In this age of internet, there is a tendency to open internet and learn from Wikipedia and similar sites. While this has its own advantages for  a mature learner, I recommend that a beginner must learn from the masters even though the learning curve may look very steep.

This collection is an attempt to encourage younger generation to leart role of contibuting  to the subject and from the very best.

There are many who contributed to pedgogy and teaching. Many old texts become 'obsolete' simply because is it fashionable to go for the latest.  It would be foolhardy to ignore these and other works, so we include here snippets and quotes etc. from many other sources too.

It is  hoped this will provide incentive to the younger generations to ask for more.

"Choose the very best from every one"

20-02-08 16:02:30 n

### [LSN/Cm-02001] Euler Lagrange Equations of Motion

Node id: 4357page
22-03-31 00:03:07 n

### [LSN/ME-06001] Potential Problems in One Dimension

Node id: 4131page
22-03-29 20:03:00 n

### [NEWB/EM-03] Electric Potential

Node id: 5909page

Last Updated May 8, 2023

23-05-08 08:05:21 n

### [NOTES/ME-06005] Bounded Motion --- Oscillations Around Minimum

Node id: 5681page
24-04-08 07:04:01 y

### [QUE/SM-03001] SM-PROBLEM

Node id: 5065page

Consider a system of $N$ atoms. Assuming that they can exist in two states only. The ground state having energy zero and an excited state having energy $\epsilon$.

• Find the number of micro states with total energy $U$.
• Write an expression for entropy and using Stirling approximation for the factorial $$\ln (N!) \approx N \ln N - N$$ find the temperature of the system and hence show that $$U = \frac{N\epsilon}{1+ e^{\epsilon/kT}}$$
• What is fraction of atoms are in the excited state at very large temperature $(T >> kT)$?
22-01-13 18:01:58 n

### [QUE/SM-03005] --- SM-PROBLEM

Node id: 5069page

A system consists of three particles and each particle can exist in five possible states. Find the total number of microstates and the number of microstates that energy level has two particles assuming

• the particles are non-identical
• are identical bosons
• are identical fermions.
22-01-09 20:01:30 n

### [QUE/VS-02008]

Node id: 3710article

PRO/VS-02008
Consider the set of all vectors $$\xi=(\xi_1,\xi_2,\xi_3)$$ in $$C^3$$ for
which

1. $$\xi_1$$ is real
2. $$\xi=0$$
3. $$|\xi_1|> 0$$
4. either $$\xi_1$$ or $$\xi_2$$ equal to zero
5. $$\xi_1+\xi_2=0$$
6. $$\xi_1+\xi_2=1$$

Give the dimensions of the vector spaces, wherever appropriate and give a
possible basis

22-04-22 16:04:24 n

### [QUE/VS-02009]

Node id: 3711page

PRO/VS-2009

Consider the set of all vectors $$3\times3$$ real matrices $$A$$ for which

1. $$\text{Tr}(A)=0$$
2. $$\det A=0$$
3. $$A_{11}>0$$
4. either $$A_{11}, A_{22}, A_{33}$$, all equal to zero
5. $$A^{\text{T}}=A$$
6. $$A^\text{T}=-A$$

Give the dimensions of the vector spaces wherever appropriate and give a possible basis?

22-04-22 16:04:31 n

### [QUE/VS-02010]

Node id: 3712page

PRO/VS-02010

Consider the set of all polynomials $$p(t)= a_0 +a_1 t + a_2 t^2$$ for which

1. $$p(0)=0$$
2. $$2p(0)=p(1)$$
3. $$p(t)=p(1-t)$$
4. $$p(1) > 0$$.

Give the dimensions of the vector spaces wherever appropriate and give a possible basis?

22-04-22 16:04:07 n

### [QUE/VS-02011]

Node id: 3713page

PRO/VS-02011

Consider the linear span of the vectors (1,0,0), (1,1,0) and (1,-1,0).
What is the dimension of the vector space thus obtained?

22-04-22 16:04:41 n

### [QUE/VS-02012]

Node id: 3714page

PRO/VS-02012

Do the polynomials $$p_1(t)= 1-t, p_2(t)=t(1-t), p_3(t)=1-t^2$$ give a basis for vector space  $$P_2(t)$$ all polynomials ?

22-04-22 16:04:44 n

### [QUE/VS-03001]

Node id: 3742page

In $$M^3(C)$$ consisting of all $$3\times3$$ complex matrices $$A= \begin{pmatrix} A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \\ A_{31} & A_{32} & A_{33} \end{pmatrix}$$ which of the following are linear functionals?

1. $$\phi(A) = \text{Tr}(A)$$
2. $$\phi(A)= \text{Tr}(a) + \text{Tr}(A^T)$$
3. $$\phi(A) =\det (A)$$
4. $$\phi(A)= A_{11}+A_{21} + A_{31}$$
5. $$\phi(A) = A_{11}.$$
6. $$\phi(A)= A_{12}A_{32}$$
22-04-22 15:04:40 n

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