# Search results

1. ### I Form factors and Interaction term of the Action

Consider, two fields interact with each other and the interaction term of the action is given. Now the Lagrangian density is fourier transformed and the interaction term of the action is expressed as an integral over the momentum space. How is the integrand related to the form factor?
2. ### I Transformation of Lagrangian

Consider a Lagrangian: $$\mathcal{L} = \mathcal{L}(q_1\, \dots\, q_n, \dot{q}_1\, \dots\, \dot{q}_n,t)$$ From this Lagrangian, we get a set of ##n## equations: \frac{d}{dt}\frac{\partial \mathcal{L}}{\partial \dot{q}_i} - \frac{\partial...
3. ### Green's function of a PDE

Homework Statement Find out the Green's function, ##G(\vec{r}, \vec{r}')##, for the following partial differential equation: $$\left(-2\frac{\partial ^2}{\partial t \partial x} + \frac{\partial^2}{\partial y^2} +\frac{\partial^2}{\partial z^2} \right) F(\vec{r}) = g(\vec{r})$$ Here ##\vec{r}...
4. ### Two successive rotation (Goldstein problem 4.13)

Homework Statement Suppose two successive coordinate rotations through angles ##\Phi_1## and ##\Phi_2## are carried out, equivalent to a single rotation through an angle ##\Phi##. Show that ##\Phi_1##, ##\Phi_2## and ##\Phi## can be considered as the sides of a spherical triangle with the angle...
5. ### I Experiment: Spin Rotation Operator

How do we experimentally apply the operator ## \exp{\left(-i\phi\frac{ S_z}{\hbar}\right)}## on a quantum mechanical system? (Here ##S_z## is the spin angular momentum operator along the z-axis) For example, on a beam of electrons?

7. ### I Four-vector related to electric and magnetic dipole moment

What is the four-vector related to electric and magnetic dipole moment?
8. ### I Does measurement change the energy of a system?

Suppose, the energy of a particle is measured, say ##E_1##. So now the state vector of the particle is the energy eigenket ##|E_1>##. Then the position of the particle is measured, say ##x##. As the Hamiltonian operator and the position operator are non-commutative, the state vector is changed...
9. ### How many equations does a physicist write in his lifetime?

How many equations does a physicist write in his/her lifetime on average? Is there any approximate statistics on this? Also how much is this correlated to his/her contribution to physics?
10. ### I Particle in a box problem

Consider the particle in a box problem. The number of energy eigenbasis is 'countable' infinity. But the number of position eigenbasis is 'uncountable' infinity. x can take any value from the interval [0,L] Whichever basis I choose, shouldn't the dimensionality of the vector space be the same?
11. ### I Is Second rank tensor always tensor product of two vectors?

Suppose a second rank tensor ##T_{ij}## is given. Can we always express it as the tensor product of two vectors, i.e., ##T_{ij}=A_{i}B_{j}## ? If so, then I have a few more questions: 1. Are those two vectors ##A_i## and ##B_j## unique? 2. How to find out ##A_i## and ##B_j## 3. As ##A_i## and...

14. ### I Dirac Delta using Fourier Transformation

We know, $$\delta(x) = \begin{cases} \infty & \text{if } x = 0 \\ 0 & \text{if } x \neq 0 \end{cases}$$ And, also, $$\int_{-\infty}^{\infty}\delta(x)\,dx=1$$ Using Fourier Transformation, it can be shown that, $$\delta(x)=\lim_{\Omega \rightarrow \infty}\frac{\sin{(\Omega x)}}{\pi x}$$ Let's...
15. ### Fourier series

Homework Statement Can the following function be represented by a Fourier series over the range indicated: $$f(x) = \cos^{-1}(\sin {2x}),~~~~-\infty<x<\infty$$ Homework Equations The Dirichlet conditions that a function must satisfy before it can be represented by a Fourier series are: (i) the...
16. ### I Contraction of mixed tensor

Is that true in general and why: $$A^{mn}_{.~.~lm}=A^{nm}_{.~.~ml}$$
17. ### I Two metric tensors describing same geometry

Consider two coordinate systems on a sphere. The metric tensors of the two coordinate systems are given. Now how can I check that both coordinate systems describe the same geometry (in this case spherical geometry)? (I used spherical geometry as an example. I would like to know the process in...
18. ### Complex Integration using residue theorem

Homework Statement [/B] ##C_\rho## is a semicircle of radius ##\rho## in the upper-half plane. What is $$\lim_{\rho\rightarrow 0} \int_{C_{\rho}} \frac{e^{iaz}-e^{ibz}}{z^2} \,dz$$ Homework Equations If ##C## is a closed loop and ##z_1, z_2 ... z_n## are the singular points inside ##C##...
19. ### Physics Jokes?

What are your favorite Physics jokes? One of my favorite is : Studying Entropy is a TdS PdV. My friend, Fahim Bin Selim, first told me this joke.
20. ### Most Beautiful Theory?

What's the most beautiful theory in Physics or Math you have ever read? For me, they are the Prime Number Theorem and the Theory of Relativity.
21. ### I Isn't the force calculated twice?

Isn't the force calculated twice here? For example, the force along AB is at first calculated for the resultant force along OB, then for the resultant force along AC. I think the compression and tensile stress should be ##\frac{F}{2a}##.
22. ### B Adiabatic but permeable piston

How can a permeable piston be adiabatic? If substances can go in and out of the cylinder and the substances have heat energy, heat can be exchanged through a permeable piston. I came across this term in the book, but cannot understand.
23. ### I Demagnetizing effect of toroids or long thin cylinders

I read in the book, "Experiments on paramagnetic materials are usually performed on samples in the form of cylinders or ellipsoids, not toroids. In these cases, the value of the magnetic field inside the material is somewhat smaller than the value of magnetic field generated by the current in...
24. ### Temperature dependence of Cv at very large volume

Homework Statement In the case of a gas obeying the equation of state \begin{align}\frac{Pv}{RT}&=1+\frac{B}{v}\end{align} where ##B## is a function of ##T## only, show that, \begin{align}c_v&=-\frac{RT}{v}\frac{d^2}{dT^2} (BT)+\left(c_v\right)_0\end{align} where ##\left(c_v\right)_0##...

27. ### Prove dQ is an inexact differential

Homework Statement ##dz=Mdx+Ndy## is an exact differential if ##(\frac{\partial M}{\partial y})_x=(\frac{\partial N}{\partial x})_y##. By invoking the condition for an exact differential, demonstrate that the reversible heat ##Q_R## is not a thermodynamic property. Homework Equations...
28. ### Problem on Thermodynamics

Homework Statement Derive the equation ##U=-T(\frac{\partial A}{\partial T})_V## where ##U## is the internal energy, ##T## is the temperature, ##A## is the Helmholtz function. Reference: Heat and Thermodynamics, Zemansky, Dittman, Page 272, Problem 10.4 (a) Homework Equations ##dA=-PdV-SdT##...
29. ### Problem about an Eigenvector

Homework Statement If ##AA^T=A^TA##, then prove that ##A## and ##A^T## have the same eigenvectors. Homework Equations The Attempt at a Solution ##Ax=\lambda x## ##A^TAx=\lambda A^Tx## ##AA^Tx=\lambda A^Tx## ##A(A^Tx)=\lambda (A^Tx)## So, ##A^Tx## is also an eigenvector of ##A##. What should...
30. ### Electric field outside conductor

Homework Statement A long metal pipe of square cross-section is grounded on three sides, while the fourth (which is insulated from the rest) is maintained at constant potential ##V_0##. What is the electric field just outside the section opposite to ##V_0##? Homework Equations The Attempt at...