Recent content by Samuel Williams

Yes, the mainline frequencies are the corresponding 1.6GHz and 6 GHz as seen. They are referred to as mainline because F = constant for their transitions. Are you referring to thermal excitation, or something with regards to blackbody radiation such as Wien's law? I don't think that is...

Hi all, the question is as follows: 1. Homework Statement From the energy level diagram for OH in the study guide, it can be seen that the first rotationally excited level of OH (2∏3=2 J =5\2) lies 120 K above the groundstate. What is the wavelength of radiation associated with a transition...

There is no frequency given, so I'm "assuming" we can take any value and essentially work under any ideal conditions that would provide such waves. I have been googling for a while which is why I decided to post here. There are a few good ones, but they seem to refer mainly to electromagnetic...

I haven't really thought about that to be honest, since the section of work is with regards to plasma and magnetized plasma.

Not that I am aware of, which is why I believe it to be possible. The question is as given with no further details or information.

Homework Statement Are longitudinal magnetic waves possible? Give reasons for your answer. Homework Equations Working with Maxwell's equations, Lorentz force, electrostatic and electromagnetic waves in plasma. The Attempt at a Solution No idea whatsoever. I believe it is possible based on...

Homework Statement Consider a particle of spin 3/2. Find the matrix for the component of the spin along a unit vector with arbitrary direction n. Find its eigenvalues and eigenvectors. Homework Equations I know that the general spin operator is \begin{equation} \widehat{S} = a\cdot...

I managed to figure out where I have been going wrong thanks to you. I have been using Euclidean inner products instead of Hermitian inner products. Thanks for the help

The eigenvalue should have a -, must have missed it. I already normalized the vectors, giving 1/√(1-i)*((1−i√2) 0 1)) And it still doesn't seem to work out for me

Question Consider the matrix $$ \left[ \matrix { 0&0&-1+i \\ 0&3&0 \\ -1-i&0&0 } \right] $$ (a) Find the eigenvalues and normalized eigenvectors of A. Denote the eigenvectors of A by |a1>, |a2>, |a3>. Any degenerate eigenvalues? (b) Show that the eigenvectors |a1>, |a2>, |a3> form an...

Let (X, d) be a complete metric space, and suppose T : X → X is a function such that T^2 is a contraction. [By T^2, we mean the function T^2 : X → X given by T^2(x) = T(T(x))]. Show that T has a unique fixed point in X. So I have an answer, but I am not sure whether it is correct. It goes as...

Use inclusion-exclusion to find the number of ways to arrange the six numbers 1, 2, 3, 4, 5, 6 such that either 1 is immediately followed by 2, or 3 is immediately followed by 4, or 5 is immediately followed by 6. I believe that this can be solved using unions. By setting the sets to be the...

Thanks, I managed to find a solution to the problem with your explanation to the question.

Again, my apologies. It seems that I accidentally deleted the image. So these are the questions I did (a) and (b) as mentioned above and there are no relevant formulae or theorems that I am aware of for part (c).

My apologies for having to post in an image, my latex skills are not good enough for the question at hand :( a) There is no solution since the system has more unknowns than equations (the equations are equal giving 1=2 which does not make sense). b) I get a solution of \begin{bmatrix}1 \\1 \\...