Thanks, i fully understand now, using the derivation of Pauli spin matrices from last semester i can see how trace works, its just that our lecturer this semester has not really written anything out in matrix form, he's just mentioned it in passing.
Thankyou for that, that clears up a lot of my misunderstanding. In lectures it's been mentioned that trace is the same as summing the diagonal elements of a matrix, however what matrix are we referring to here? So the density operater describes the probabilities of certain states, how is this...
Hi, im just starting a 3rd year course in Statistical Mechanics, and am a bit confused about the operator trace, Tr. I know there is a trace for quantum operators, as well as one in classical physics, but i am not sure how to calculate either, or their physical meaning. Any help would be great...
Suppose we have a polarized object, and wish to calculate D(r) using
D(r) = epsilon E + P
Do we have to account for the electric field that the polarized object creates, or is it enough to just use the electric field which created the polarization?
Yes that sounds great, but i have not yet studied any QFT, just QM and statistical mechanics. Anyway my attempt is to use the Grand Canonical Partition function, but since in this question the particle number is fixed, i set the chemical potential equal to zero.
However the question wants to...
I am wondering how i would go about calculating the canonical partition function for a system of N quantum harmonic oscillators. The idea of the question is that we are treating photons as oscillators with a discrete energy spectrum. I'm confused as whether to use Maxwell-Boltmann...
We have only just been introduced to Dirac notation, and have not had a lot of experience in linear analysis and dual vector spaces etc... I have figured out how to do it, i just contract |g> with an arbitrary bra <h|, then do the same with <g| and an arbitrary bra |h>, show the two are...
I am trying to show that |g> = A|f> implies
<g| = <f|B
where A is an operator and B is its Hermitian conjugate.
I think my problem is with notation, but i have not been able to show this as yet.
The double slit experiments, similar to Feynman's thought experiments, illustrate the distributions of particles, or waves as they enter the double slit apparatus, so the shape of the slits will not affect the experiment, neither does the fact it is in a vacuum or not.
If we fire particles at...
It is the equations of motion that are invariant under the addition of a function that is the total time derivative of some function, to the Lagrangian. Since the Euler-Lagrange equations involve derivatives with respect to position and velocity only, a partial derivative wrt to position or...
As far as i know there isn't, and there are no answers in the back, i used this text for my 2nd and 3rd year electrodynamics courses. If you google it, some universities have solutions to select questions, as these are often set as assignment questions.
I am wondering how to physically interpret the generalized momentum quantity derived from the Euler-Lagrange equations. For some Lagrangians is it equal to the actual momentum for the particle, however i have noticed that for a relativistic particle moving in an electromagnetic field the...
Why must a group of order 98 contain a subgroup of order 7?
I would think that Sylow's 1st theorem implies there exists at least one Sylow-7-subgroup of order 49 and at least one Sylow-2-subgroup of order 2 (since 98=2x7x7).