I am in the rather unique and exciting position of being able to design an extension curriculum for some gifted Physics students who are in their final year of high school. The goal of the curriculum is to help prepare them for university physics with tools and ways of thinking, without just...
Thanks! I can see now that as the ring falls deeper, the angle light from the ring makes with the boundary between the two media approaches 90, and therefore the angle that the light ray makes with the other side of the boundary approaches the critical angle.
Homework Statement
https://gyazo.com/f8cf156e7bd2f2511e3fa859e3732fe6
Homework Equations
Snell's law.
The Attempt at a Solution
I'm mostly confused about the relevance of the second medium (of index n2) given that the distance between the ring and the boundary is "small". Having attempted to...
Hi all,
I'm a physics graduate now working as a maths and physics teacher in a sixth form college. I loved my degree, though wish I'd had the work ethic I do now when I was studying full time. I took a theoretical physics course in my 4th year (syllabus here...
What OCR wants to get at is that if you have a wire of some dimensions, doubling the length halves k without affecting YM, and having two wires (effectively doubling the cross sectional surface area) doubles k without affecting the YM. This lets you nicely draw a distinction between the YM of a...
The technical difference between virtual and real particles is that virtual particle are "off shell" meaning that their mass energy and momentum does not satisfy the relation E^2 - P^2 = M^2, however virtual particles should be thought of as a sort of mental abacus that help us calculate things...
I'd be fascinated to know how one could estimate the volume of matter in the universe without using the method I outlined above. I'd also be interested to know how you came up with that percentage.
Scientists have indeed, and you're thinking along nearly the right lines: cosmological observations allow scientists to make a reasonable estimate of the energy density of matter in the universe, and calculating the volume of the observable universe is straightforward (though interestingly, due...
"I think it's possible in principle - just very very difficult."
very very difficult is an absurd underestimate. Producing and containing 1kg of antimatter is "possible in principle" in the same way that counting every particle in the observable universe is "possible in principle".
Homework Statement
Taking the proton to be a uniformly charged sphere of radius 1 fm, ﬁnd an
expression for the change in potential experienced by the muon as compared with that
in the case of a point-like proton. Use ﬁrst order perturbation theory to calculate the
ground-state energy...
*URGENT* (Exam tomorrow morning!) Calculating a real integral using residue theorem
Homework Statement
See attached picture
http://imageshack.us/photo/my-images/827/unledozs.jpg/
Homework Equations
The Attempt at a Solution
Parts a) and b) are straightforward.
For b) I end up...
This looks interesting but i'm having quite a lot of trouble following your notation. Do you know the name of the theorem so i could look it up perhaps?
Thanks for the help.
I think I understand where I've gone wrong now. The problem is in my intuition, not in my appilcation of the pauli matrices.
as |+> = \frac{1}{\sqrt{2}}(|+_x> + |-_x>)
(where |+_x> and |-_x> are the eigenvectors of S_x with eigenvalues +/- 1/2)
when we operate with Sx we obtain...
Homework Statement
What is the result of operating on the state |+> with the operator Sx?
here, |+> denotes the eigenstate of Sz with eigenvalue 1/2. I am working in units where h-bar is 1 (for simplicity, and because I don't know how to type it)
Homework Equations
S_i = \frac{1}{2} σ_i...
Homework Statement
Find the eigenvalues/vectors of A. (I can do this bit :P, A is a 3x3 matrix)
What are the eigenvalues and eigenvectors of the matrix B = exp(3A) + 5I, where I is
the identity matrix?
Homework Equations
The Attempt at a Solution
I have (correctly) found that A...
Homework Statement
Show that the change in internal energy of a simple system between states (V1, T1)
and (V2, T2) is given by
∆U = \int^{T1}_{T2} C_v\ dT + \int^{V1}_{V2} T.\frac{\partial p}{\partial T}|_V - p \ dV
Homework Equations
dU=dQ-pdV
The Attempt at a Solution
As U is a function...
You have the correct shape, however you may define a value at x= 0, 1, 2 for the heavside step function. Personally I think 1/2 is the most sensible, because it means that the function is odd and the approximation H(x)={1+tanh(kx)}/2 holds exactly in the limit k->infinity.
0, 1 and 0.5 are all...
I *think* it's because you're redefining u->t. Normally when using a substitution you just either substitute back in at the end or change the limits over which you are integrating. If you redefine u so it is a times smaller than it was before, you also need to make sure all the constants are...
Homework Statement
solve
(z+i)^5 + (z-i)^5 = 0
Homework Equations
The Attempt at a Solution
I have found the five possible values for z by expanding the original expression into powers of z and i. The imaginary terms cancel exactly, leaving a cubic equation in z which is easily solvable...
I *think* the question is asking "should the probability of the system being in a particular configuration be the same as is stated in PEEP" but that doesn't seem right.
Is there a typo in your version of the question? It's very hard to understand what you're being asked for.