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In section 18.7 of Bruus & Flensberg the authors provide a microscopic derivation of the Josephson effect. The hamiltonian on both sides of the tunnelling junction is just the typical BCS hamiltonian, on one side (with fermion operators ##c##) $$ H_c = \sum_{k,\sigma} \epsilon_k...

It seems like I overlooked the simple fact that the state cannot change during a sudden, ##\textit{finite}## perturbation, so I was right in assuming that the spin would be ##|+\rangle## at ##t=0^+##. To understand why the system's state must be continuous over the sudden perturbation in the...

Consider an uncharged particle with spin one-half moving with speed ##v## in a region with magnetic field ##\textbf{B}=B\textbf{e}_z##. In a certain length ##L## of the particle's path, there is an additional, weak magnetic field ##\textbf{B}_\perp=B_\perp \textbf{e}_x##. Assuming the electron...

One last question, the Unruh modes as defined in Sean Carroll's "Spacetime and Geometry" are: $$h_k^{(1)} = \frac{1}{\sqrt{2\sinh(\pi \omega/a)}}\big(e^{\pi \omega/2a} g_k^{(1)} + e^{-\pi \omega/2a} g_{-k}^{(2)}{}^*\big)$$ On the other hand this paper gives a different definition: $$h_k^{(1)} =...

I see, thanks!

But couldn't the left moving negative frequency modes be analytic in that half of the complex plane?

In Carroll "Spacetime and Geometry" I found the following explanation for why the analytically extended rindler modes share the same vacuum state as the Minkowski vacuum state: I can't quite understand why the fact that the extended modes [\tex]h_k^{(1),(2)}[\tex] are analytic and bounded on...

Thanks for the answers, very enlightening!

In p.385 of Griffiths QM the vector potential ##\textbf{A} = \frac{\Phi}{2\pi r}\hat{\phi}## is chosen for the region outside a long solenoid. However, couldn't we also have chosen a vector potential that is a multiple of this, namely ##\textbf{A} = \alpha \frac{\Phi}{2\pi r} \hat{\phi}## where...

Thanks, very clear explanation!

So the so-called act of measurement in the OP is the painting process, not the blind man somehow "measuring" the colour of the apple? This seems to make a lot more sense now.

Thank you. Suppose then that instead of colouring apples i consider randomly assigning a spin to an electron (here surely quantum effects are coherent). If I don't observe the spin of the electron, then does this mean that the electron is in a definite spin state, but I just haven't performed a...

Thank you. So this case would fall under "incomplete information situations" rather than superpositions as you have described?

I guess my question is what makes something capable of being in a superposition, and other things not?

just because an apple isn't an elementary particle doesn't mean that it can't be in a superposition right?

But couldn't you apply that logic to an electron's spin as well? It's either spin up or spin down.

So the wave function is not a superposition, it's just that the blind man can't perform the necessary measurements?

Suppose a blind man builds a machine that paints three apples with three colors, either red, blue or green. Once the machine has done this, are the three apples in the following superposition: or is the wavefunction just one of It feels like because the man is blind, the apples should be in...

that's the way I justify it XD

The ##\sigma_z## is a diagonal matrix so to take its exponential we can simply take the exponential of the diagonal elements.

What do you mean by pulled through?

EDIT: I'M SO DUMB! I can't believe I can't multiply matrices together. Of course the result is not zero, the matrix on the left will be: $$ \begin{pmatrix} 0 & e^{i\omega_at/2}\\ e^{-i\omega_at/2}&0 \end{pmatrix} $$ So i was solving problem 3 from...

Actually fridge magnets are made like this. Here's a fun experiement to do. Take two fridge magnets and try to slide one on top of the other. In one direction the movement will be smooth, in the other it will be quite "zig-zaggy" if that makes sense. This is because fridge magnets are stacks...

So then I should not take into consideration the magnetic repulsion?

great!

also is the explanation I posted correct? I think it makes sense but you never know.

Oh, that makes much more sense...😅

For anyone interested, I believe I have found an answer to my question. It turns out that the formula I suggested: $$\tau_{left} = \tau_{0} + \textbf{R}\times \textbf{F}$$ is only correct when "left" is an inertial frame of reference. If instead we choose a point P that is accelerating, so that...

it doesn't make sense since ##\frac{d}{L}## is unitless whereas ##\frac{mv^2}{R}## has units Newtons.

the railroad is circular so the curve never ends

The solution to the problem (given by the book) is ##N_R=\frac{Mg}{2} + \frac{LMv^2}{Rd}##, so it is not a 50/50 nor a 100/0 distribution of weight.

I saw that the solution states that the torque about the center of mass is zero, since the man does not rotate about its center of mass. However, I then thought about taking the torque about the left foot (so the right foot for the man's POV). Hence: $$\tau_{left} = \tau_{0} + \textbf{R}\times...

Summary:: Griffiths problem 8.5 Problem 8.5 of Griffiths (in attachment) I already solved part (a), and found the momentum in the fields to be $$\textbf{p}=Ad\mu_0 \sigma^2 v \hat{\textbf{y}}$$ In part (b), I am asked to find the total impulse imparted on the plates if the top plate starts...

Oooh, so it has to do with Lorentz contraction? The fact that the magnetic interaction is simply a relativistic form of the electric field explains how work is being done? I might have to read up on the Lorentz transformations...

Could you kindly redirect me to those threads? I'm seriously not going to sleep without answering this question 😭

But where is the electric field?

Recently I have encountered the following expression for the potential energy of a magnetic dipole of moment ##\boldsymbol{\mu}## placed in an external magnetostatic field B: $$U=-\boldsymbol{\mu} \cdot \textbf{B}$$. However, I was told that magnetic fields are non-conservative, so we can't...

Oh ok thanks.

One question: if initially (before turning on the AC supply) there is no magnetic field outside, and then after some instants, as we saw in my diagram, there is a net magnetic field outside, this means that there must be some net change in flux right? Perhaps the moment the AC supply is turned...

Oh, I see. So exactly because the external magnetic field is decreasing, the fact that we have an induced magnetic field keeps the change in magnetic flux approximately constant, thus shielding anything behind. EDIT: Also, could you elaborate on why this causes metals to be shiny? Sounds very...

So I've been trying to figure out how EMF shielding works. More specifically, I've seen videos where placing a metal conductor in front of a circular coil (with AC running through at radio frequencies) apparently shielded anything behind it. After searching online, I repeatedly saw Eddy...

Ah that's right, the "tilt angle" also affects the magnetic flux.

My explanation: A circular coil is connected to an AC supply at a frequency of 30-50 kHz (radio frequency). Therefore, an alternate current will be running through this “primary” coil, producing an alternating magnetic field. This magnetic field periodically decreases in strength, alternating...

That is true... Well I guess I now trust Ampere's Law even more than before. Thanks

I tried just evaluating the curl in cylindrical coordinates and found 0, as was expected. Soo was my initial reasoning using Ampere's law correct? Or was it just a coincidence?

Isn't it faster to just use Ampere's Law in differential form?

Since the current density is zero outside, is the curl also zero?

do you mean the curl of the B field?

Summary:: Not sure if my solution to a magnetostatics problem is correct [Mentor Note -- thread moved from the technical forums, so no Homework Template is shown] I was trying to solve problem 2 from...

So I was watching this video containing DIY experiments on electromagnetic induction . At minute 4:45, the dude pretty much creates a transformer without using an iron core. He runs 30-50 kHz AC in a coil (forming the primary circuit) and then brings another coil with its ends attached to a...