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...
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.
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...
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...
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'...
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
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...
Are the principle of least action(see first equation) and the hamilton principle 'exactly' the same? As far as I know, yes. How do I go from one to the other
My Graduate Mechanics text (Walecka and Fetter) says in the chapter on Small Oscillations, that the Modal Matrix Diagonalizes the Lagrangian
L = \sum_{\sigma=1}^\infty (\dot{\zeta_\sigma}^2 - \omega_\sigma \zeta_\sigma^2)
where \zeta are the normal coordinates related to the original...
I need a conformal mapping that would map an ellipse or a circle to a line. I need this for the http://physics.indiana.edu/~berger/p506_fall2008/p506ps6.pdf" [Broken].
As far as I can understand, z^2 + 1/z^2 makes the geometry similar to that of a plane on the horizontal axis with a circle...
I was wondering if someone could help me with Goldstein's equation 6.3 (3rd Edition). It is the chapter of oscillations and all that he has done in the equation is to expand it in the form of a Taylor series. I can't seem to get how all those ni's come to get there.
I was trying to expand a scalar function with a power series but it accepts a vector argument. Do I simply use the multivariable power series expansion with the components of the vector acting as the argument OR do I use the single variable power series and take the vector's magnitude in the...
For a hermitian operator A, does the function f(A) have the same eigenkets as A?
This has been bothering me as I try to solve Sakurai question (1.27, part a). Some of my class fellows decided that it was so and it greatly simplifies the equations and it helps in the next part too but I don't...