Spin Definition and 1000 Threads

By the statement of the question, a solution must take the form ##\begin{pmatrix} \Psi_1 \\ \Psi_2 \end{pmatrix}## and the energy operator will be as per usual ##\hat{E} = i\hbar \frac{\partial}{\partial t}##. I am confused by the fact that ##S_y = \frac{\hbar}{2} \begin{pmatrix} 0 & -i \\ i & 0...

I read that quantum spin is the measure of the angular momentum of a quantum object. Suppose you have a rotating Thing 1. Quantum objects bounce off of it then collide with Thing 2. Will this transfer angular momentum from Thing 1 to 2, causing it to rotate?

Can four (or more) electrons form a completely antisymmetric joint spin wave function？

Hi everyone, I’ve been thinking about this for a while and have done a bit of research but can’t seem to get a straight answer. Aside from collision with another object in space, is there anything that could cause the Earth’s rotation to dramatically slow down? If a sufficiently massive object...

Hello everyone, I hope I'm asking in the correct section, if not please point me. I read a list of gravitational wave detection. I focused on black hole - black hole events and I noticed the resulting black hole spin is very similar about a=0.7. I didn't find any explanation for this. List of...

Suppose that we have a system including two single (and identical) orbitals as shown in the attached image. Then, consider the states that we have two different spins on the two orbitals. It seems that because of the left right symmetry of the system the special part of teh wave function can not...

Hi Pfs Rovelli defines spin networks in this paper https://arxiv.org/abs/1004.1780 for a trivalent node Vn = 0 (the volume) nodes begin to "get" volume with the four valent case. take a cube or a tetrahedron, each vertex is linkes to 3 nodes so they would have a null volume. things are...

According to Chapter 8 of Griffiths' book Introduction to Electrodynamics, the magnetization force that acts on a magnetic dipole is $$F_M=\nabla (m \cdot B)$$, where ##m## is the magnetic moment and ##B## is the magnetic field. For a paramagnetic or diamagnetic particle...

6.0 rev - 1 s 1 rev - 1/6 5.0 rev - (1/6) x 5 = (5/6) s = 0.833 s I do not know how to calculate the angular acceleration

I know how to construct Sy for spin = 1 case from the raising and lowering operators. I get $$ S_y=\frac{i\hbar}{\sqrt{2}}\begin{pmatrix} 0 & -1 & 0 \\ 1 & 0 & -1 \\ 0 & 1 & 0 \\ \end{pmatrix} $$ From what I have seen, the eigenspinor for $\hbar$ is found by solving $$...

I'm just starting to get into QFT as some self study. I've watched some lectures and videos, read some notes, and am trying to piece some things together. Take ##U(1)_{EM}: L = \bar{\psi}[i\gamma^{\mu}(\partial_{\mu} - ieA_{\mu}) - m]\psi - 1/4 F_{\mu\nu}F^{\mu\nu}## This allegedly governs spin...

Pin Groups are the double cover of the Orthogonal Group and Spin Groups are the double cover of the Special Orthogonal Group. Both sets of the double cover are considered to be groups, but it seems that only one of the sets of the double cover actually contains the identity element, which means...

##Z = \sum_{-i}^{i} = e^{-E_n \beta}## ##Z = \sum_{0}^j e^{nh\beta} + \sum_{0}^j e^{-nh\beta}## Those sums are 2 finites geometric series ##Z = \frac{1- e^{h\beta(i+1)}}{1-e^{h\beta}} + \frac{1-e^{-h\beta(i+1)}}{1-e^{-h\beta}}## I don't think this is ring since from that I can't get 2 sinh...

What I have done is on my Ipad that I cant upload or at least don't know how to... :/ With hope of help DJ

Hello guys, i want to ask you a question about orbital and spin dipole, and how this is going to influence diamagnetic or paramagnetic substances. So my question is: we know in a atom there is orbital and spin motion by electrons so possibly two magnetic dipoles. Is it correct to say that in...

Hi Pfs Spin networks are defined by the way their links and their nodes are equipped with SU(2) representations and intertwiners. Could you give an example of two different spin networks with the same number of nodes, links between them, the same coloring of the links (and their orientations)...

https://physics.stackexchange.com/questions/418865/why-does-an-electron-have-spin I’ve been trying to do research on this and haven’t gotten a clear answer. It sounds like they get it through particle interactions, but I may be misreading it. Is there an answer to this? And if there is, how...

When the expectation value of spin in the z direction for one particle is zero and I make measurements for an even number of particles in the same state, do I get exactly half to be spin up and half to be spin down along the z direction? More generally, what does spin expectation value for one...

Hi Pfs i found a paper: https://arxiv.org/abs/math-ph/0306059 in which the author gives a definition of spin networks it is at the bottom of page 5 the words node or vertex does not appear. what do you think of it? Does the author think that all the information is in the hilbert spaces on which...

So this expression is apparently in Sz basis? How can you see that? How would it look in Sy basis for example? The solution is following. They are putting Sz as a basis, bur how do you know that Sz is the basis here? Thanks

I have found an answer to all of them (a-e) but I don’t know how to plot the function. Thanks!

Not sure how to mark the level, I know what the math in the Einstein field equations represents (stress energy tensor, Riemann curvature etc), but have no facility in doing anything with that math. so take 2 black holes, with say 100 solar masses. A is not spinning, B is spinning at...

There is a passage in this book where I don't follow the logic; In this short quotation from 'Quantum Mechanics: The Theoretical Minimum' by Leonard Susskind and Art Friedman \mathcal{A} represents the apparatus that is performing the measurement the apparatus can be oriented (in principle) in...

Was curious at the upper limit for neutron stars, found this article stating one was found at around 700 / s https://www.newscientist.com/article/dn8576-fast-spinning-neutron-star-smashes-speed-limit/ did not see the size, the article is behind a paywall, but it would have taken a radius of...

I googled it, and almost every source I find says something like this: "These stars were then gravitationally attracted to each other to create gigantic clusters of stars enshrouded in clouds of gas. Eventually these groupings of stars come together through the attraction of gravity and...

Quantum spin is orientable so it takes place in a space with an even number of dimensions. What is that space? If the space had an odd number of dimensions, then spin in that space wouldn't be orientable. But quantum spin is orientable. We could say that it is Minkowski space, but that space...

In the paper C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573 about quantum dots, it is stated that the basis vectors in the space of quantum states for a single cell...

Spin Launch is a proposed method, as a first stage for launching small payloads into orbit, using a slingshot method. There seems to be a video of a successful one-third scale test. Would the numbers add up, though and would it be better than an ordinary first stage vehicle? One advantage could...

Well, the problem is that, someone told me that a ball won't roll when sliding down a frictionless slope because the resultant force mgsinx is parallel to the slope which means that the ball will slide down the slope. Now, replace the ball with a round headed rod, does this means that the rod...

From Dr. Leonard Susskind's Stanford Lecture: Quantum Entanglement, Lecture 4, he sets up a "given particle is spin up along n (arbitrary direction) and discusses : what is probability we measure up along another arbitrary m directionHe does all of the setup, - calculates the eigenvectors and...

I'd like to know if this Hamiltonian ##\hat{H}=\frac{p^2}{2m}+\frac{1}{2}m\omega^2r^2+\frac{A}{\hbar^2}(J^2-L^2-S^2)## is separable into two parts ##H_1=\frac{p^2}{2m}+\frac{1}{2}m\omega^2r^2## and ##H_2=\frac{A}{\hbar^2}(J^2-L^2-S^2)## and ##[H_1,H_2]=0##. Here A is a constant. I did so...

Do all the planets in all the solar systems in our Galaxy spin in the same direction ? Clockwise or anti clockwise depending on the viewers POV.

Angular momentum is related to rotations. Momentum is related to spatial translations. Energy is related to temporal translations. Is spin related to anything? I only know the introduction to NRQM from Griffiths' book.

Let's take a beam of spin 1/2 particles prepared in the state |up> in the Z direction, let's pass it through a Stern& Gerlach apparatus in the X direction to get two beams of spin |right> and spin |left>, and then redirect these two beams directly in another inverted S&G to reunite them in one...

I've tried to use the 1st equation as a matrix to determine, but it clearly isn't a diagonal matrix. My guess is that I need to find the spin matrix along the direction ##\hat{n}##, but do I need to find the eigenstates of ##\sigma \cdot \hat{n}## first and check if they form a diagonal matrix...

So we know [Sz, Sx] = ihbar Sy (S with hats on) so what happens if you get [Sx, Sz]? Is it the same result? Just trying to work out if I've gone wrong somewhere

The spin-foam approach to quantum gravity is part of the class of approaches, that also include loop quantum gravity and a variety of other methods, that sets out to quantize space-time rather than the gravitational force itself. But, according to a new paper, it turns out that "the continuum...

My answer so far in |S| = √3 /2 *hbar but the question states it must be an angular momentum. Is this an angular momentum or am I missing something? Thanks

I tried to code spinoperators who act like $S_x^iS_x^j$ (y and z too) and to apply them to the states, which works fine. I am not sure about how to code the expectation value in the product Space. Has anyone pseudo Code to demonstrate that?

I know that we can change the spin orientation of a spin 1/2 particle up or down and test it in the Stern Gerlach apparatus. And the spin 1/2 particles need two full rotations to return to the previous state. Questions: 1). what does state mean? 2). Is, Changing spin orientation to up or...

The Kerr solution describes the gravitational field of a rotating black hole. Oftenly, the hole is said to be „spinning“, what appears as misleading to me. My questions: 1.) Is it correct to say that angular momentum in this way is treated like orbital angular momentum, not like spin? 2.) Can...

In the article by E. Majorana "Oriented atoms in a variable magnetic field", in particular, it's considered (and solved) the problem of describing a state with spin J using 2J points on the Bloch sphere. That is, if the general state of the spin system , (1) then, according...

My Bachelor thesis is all around Excitons (specifially transitions between excitons of different energies). During my work I often had trouble with the spin and the wavefunction of them. Is there maybe some good (free) literature about the theory of excitons ? I found some books in the internet...

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...

I apologize for the simple question, but it has been bothering me. One can write a relationship between groups, such as for example between Spin##(n)## and SO##(n)## as follows: \begin{equation} 1 \rightarrow \{-1,+1 \} \rightarrow \text{Spin}(n) \rightarrow \text{SO}(n) \rightarrow 1...

Every rotation in O(n) seems like it should map to spin(n) even if some rotations are not continuously connected to the identity.

Hi, this is my first thread :) I am doing my PhD about polariton in microcavities. I was just reading about the polarization of polaritons (a cuasi-particle mixing photons with semiconductors excitons) in GaAlAs microcavities. So a lot of concepts appear: pseudo-spin, chiriality, TE-TM...

If I am unable to distinguish the spin of a particle in an absence of an electric field or magnetic field, how am I able to determine whether there is an electric or magnetic field in a real-life context? How is it that we can be sure of the uncertainty of the spin of particles if we are unable...

Hello! I am trying to analyze some diatomic molecular spectra (I am using pgopher) between a ##^2\Sigma_{1/2}## and a ##^2\Pi_{1/2}## level. Before diving into tying to assign lines by eyes in pgopher I was thinking to use this Combination Differences method, but I am not sure I can do it in my...

To elaborate that summary a bit, suppose ##\mathcal H## is the Hilbert space of the particle, with ##\mathcal{H}_2\subseteq\mathcal{H}## its two-dimensional spin subspace. Now consider any ##|x\rangle\in\mathcal{H}## such that ##|x\rangle\perp\mathcal{H}_2##, i.e., ##\forall ~...