Homework Statement
Is the index notation in Srednicki's 34.16 correct given what he does in 35.29.
Essentially, in going from 34.15 to 34.16, when taking the hermitian conjugate, he does not remove the dots. In going from 35.27 to 35.29, he has done so (the dot on 'a' has moved over onto...
Thanks a lot. Now I have just two short questions:
(1) In the last expression with the string of equalities, could you have expanded the bracket differently. Meaning that instead of \eta_{\mu\rho}\Lambda^\rho{}_\sigma\omega^\sigma{ }_\lambda(\Lambda^{-1})^\lambda{}_\nu , would it had been...
Can anyone explain to me why in going from (2.4.7) to (2.4.8) the indices on the LT are arranged in the way they are. Why is mu the first index (lower) and rho the second (upper)?
Could they have been arranged in any other way? From the rules that I know, they can.
Well. To put it in another way. How would the boundary conditions change in case the sheets were made out of dielectrics. As far as I understand, there cannot be any difference.
Thanks a lot for answering. I had given up on it.
Homework Statement
Two infinitely long perfectly conducting planes at x = 0 and y = 0 form a boundary on the upper right quadrant (x > 0, y > 0). A magnetic dipole m = m_x + m_y [with their corresponding unit vectors] is located at at (x', y', z' = 0) in the upper right quadrant. Find the...
Homework Statement
Not a homework question. I need the solution to this to model another problem.
We all know the potential for the electromagnetic dipole dipole interaction (e.g. see Jackson)
I want to know if there is a solution to the problem in which there are several replicas of the two...
Homework Statement
Pathria 2.6 (2nd Edition): Phase space volume of a simple pendulum.
The total energy can be expressed in the form of the time derivative of the angle + the Sin^2 of that angle.
From this I want to calculate the phase space volume. Mathematica gives the solution in the...
Homework Statement
I need some guidance concerning Jackson 6.5c. Specifically I cannot get the -1/3 factor that the statement says I should.
Homework Equations
Solutions to part a and b which are given in the problem statement.
The Attempt at a Solution
-I started from the volume...
For a while you had me worried :)
I can change the limits later of course but I wanted to know how to solve that wretched integral. But I do think that the problem allows me to consider a point in a single plane.
In any event, it seems that I am on the right track and only need to solve...
Pretty sure that you have to and for two reasons:
[1] Wiki says that its for time varying currents and charges without ever mentioning finiteness
[2] Just saw that Griffiths example 10.2 solves for an infinite line current as well. However, the time dependence over there is not sinusoidal
Homework Statement
The question concerns a square loop in the presence of an infinitely long sinusoidally varying line current.
The complete problem is http://physics.indiana.edu/~berger/p506_fall2008/p507ps11.pdf" [Broken]
Homework Equations
The retarded potential.
The Attempt at a...
I was (implicitly) under the impression that the rho calculated would be valid for the surface as well. Could you kindly give me a physical reason for its not being valid at the surface.
Regards
Homework Statement
Jackson 6.4b
Homework Equations
Multipole expansion especially Eq 4.9 in Jackson which is for a Quadrupole
The Attempt at a Solution
I found the result in 6.4a. The rho over there tells us that there is a charge density inside the sphere. Since the charge density...
Homework Statement
This is Pathria (2nd Ed) 1.6 and it seemed simple enough but the magnitude of the answer seems unbelievably large:
A cylindrical vessel 1 m long and .1 m in diameter is filled with a monoatomic gas at P = 1 atm and T = 300 K. The gas is heated by an electrical discharge...
Homework Statement
I cant seem to figure out how he writes down this equation. Specifically:
a. Isn't Theta' = 90 degrees. Then why doesn't he write it out explicitly.
b. Whats the use of adding the Sin(Theta') if he is going to use a delta function using the Cos
c. What is the radius 'a'...
That clears up a lot in my foggy brain but there are still some issues. The y in the integral. Is this the complex part of the variable in the contour integral. i.e. z = x+iy. Or is it just some arbitrary variable. I thought that it was not connected to the integration variable in the contour...
Homework Statement
lim_{\alpha\rightarrow 0} \int_{-\infty}^{\infty} dx. e^{ixy}/(2\Pi i (x-i \alpha)) = H(y)
where H(y) is the step function ie. H(y) = 1 for y > 0, H(y) = 0 (otherwise)
Compute using an appropriate contour integral.
Homework Equations
-Laurent series
-Residue...
Can anyone explain to me how Jackson goes from equation 5.20 to 5.21 (Magnetostatics - Derivation of the curl of B in terms of the current density).
He says that he's used integration by parts but I cant see how he got rid of the first term (the one that involves integrals only) when...
Homework Statement
Can anyone tell me why Pauli Matrices remain invariant under a rotation.
Homework Equations
Probably the rotation operator in the form of the exponential of a pauli matrix having an arbitrary unit vector as its input. It may also be written as:
I*Cos(x/2) - i* (pauli...
Homework Statement
Check out problem 5.7 part a
I want to express the exterior gravitational potential in terms of the Euler angles so that I might eventually use (dV/dB)B=B0 = 0 - the condition for equilibrium.
I am therefore expecting the Lagrangian to be cyclic in terms of the other two...
A beginner to Mathematica's question:
I try to make the following integration in mathematica 6 and I get back the same expression with the integration symbol next to it. Why?
Integrate[exp[-k*z]*BesselJ[0, k*a]* BesselJ[1, k*a], {k, 0, Infinity}]
Integrate[Sin[k], {k, 0, 1}] however gives...
Can anyone tell me what is the sum of a finite series of Sines.
\sum_{n=1}^N \sin^2 (n \phi) . I am going through a text and it gives it as (N+1)/2. I tried to derive it. The N comes out ok when you use the half angle identity but I can't figure out a general rule for the Cosines that appear
I tried that as well. For example I started with Griffiths 2.153:
E_n + V_o = (n^2 \pi^2 (h/2\pi)^2)/(2 m (2a^2)) but not only that V_o is approaching infinity but also that a is approaching 0. My attempt to make it so that the product of 'a' and V_o become a constant have been fruitless.
Homework Statement
I have to show that the delta function bound state energies can be derived from the finite square well potential.
Homework Equations
The wave functions in the three regions for the finite square well. (See wikipedia)
The Attempt at a Solution
1. I start from the...