What is Spin: Definition and 1000 Discussions

Why can't the general state, in the presence of coupling, take the form $$\psi_-(r)\chi_++\psi_+(r)\chi_-$$ where ##\psi_+(r)## and ##\psi_-(r)## are respectively the symmetric and anti-symmetric part of the wave function, and ##\chi_+## and ##\chi_-## are respectively the spinors representing...

Can an electron in a spherically symmetrical potential energy function have non-zero spin angular momentum?

Representation (n,n)=nxn=2n+(2n-1)+...+2+1 , where + is direct sum, and x is tensor product. Trace of (n,n) is zero because tr(k) is zero, where k=1 to n. But why tensor (n,n) is symmetric tensor of rank 2n? I read Weinberg book Vol. 1 page 231. But he don't clearly says this .

I will refer to the spin example outlined in the opening chapters of the Theoretical minimum. Suppose we prepare a spin with a z component of +1. If we rotate the apparatus about 180 degrees, the ‘classical component’ of the prepared spin vector along the new axis of the detector is -1, so...

What are the rules to write Pauli's spin matrices in higher-order matrices (especially in 4x4 matrices)

first of all, I tried to obtain the energy eigenvalues of the Hamiltonian, by using the equation ##det(\hat H -\lambda \hat I)=0## ##\gamma V\delta(z)(\hat z \times \mathbf{p}) \cdot \sigma=\gamma V\delta(z)(p_x\hat j-p_y\hat i)\cdot(\sigma_x\hat i + \sigma _y \hat j)=\gamma...

I know there are numerous threads on this and I have read quite a bit such as EPR and Bell's inequality. I hope I can ask this the right way: A particle has 0 spin and gives off two children particles with spins -1/2 and +1/2 (we don't know which is which yet, or they have to end up this way...

I did the first part using the transfer matrix method: $$ Z = Tr(T^{N}) $$ In this case, the transfer matrix will be $$ T(i,i') = \begin{pmatrix} e^{\beta J} & 1 & e^{-\beta J}\\ 1 &1 &1 \\ e^{-\beta J} & 1 & e^{\beta J} \end{pmatrix} $$ To get the trace of $T^N$, you find the...

Suppose I have a system of two (possibly interacting) spins of 1/2. Then the state of each separate spin can be written as a ##\mathbb{C}^2## vector, and the spin operators are made from Pauli matrices, for instance the matrices ##\sigma_z \otimes \hat{1}## and ##\hat{1} \otimes \sigma_z##...

My question may include condensed matter physics concepts but my main question is related to quantum mechanics in general, that's why I posted it here.In fact I'm working on an condensed matter physics paper, where we are dealing with a two-metal system. The interface between the two metals is...

Let's consider Bohm's paradox (explaining as follows). A zero spin particle converts into two half-spin particles which move in the opposite directions. The parent particle had no angular momentum, so total spin of two particles is 0 implying they are in the singlet state. Suppose we measured Sz...

We are given the wave function with spin, but it doesn't say in which Ylm each spin X± goes. So how do I know? Examples; (1) Ψ = 1/√3 R21(r) ( Y10 √2Y11 ) Here we have the up Spin X+ to Y10 and the X- to Y11 I notice the X- went to...

Hello, I'm trying to couple 3 spin 1/2 particles. So far, I have been able to find the coefficient for the other states but I can't get the results for ##j_{12} = 0## to ##j_3=1/2##. Here is my attempt: 1) Using CG table...

Hey Guys/Gals i understand the general premise of this question and can calculate the solution but i am a bit confused. I am supposed to represent a generic state as a linear combination of the |-,x> , |+,x> basis vectors. However i don't know why, is the question actually asking for the...

Problem: Here’s a little Monte Carlo challenge problem, Consider the following game, which uses the two spinner disks. Suppose a player spins one or the other of the pointers on the disks according to the following rules: (1) if the player spins pointer ##i## and it stops in the region with area...

How do the Pauli spin matrices transform under an inversion ? I think I mean to say the 3 dimensional improper rotation which is just in 3 dimensional matrix notation minus the identity - so exactly how are the 2 dimensional Pauli spin matrices changed. And under a 180 rotation do the 'y' and...

Why does the derivation of the Dirac equation naturally lead to spin ½ particles? The equation is derived from very general starting assumptions, so which of these assumptions has to be wrong to give us a spin-0 or spin-1 particle? I have tried to search for an answer and got as far as this...

Recently, I want to study spin relaxation in graphene, but I don't know how to get start. Can anyone tell me which papers should I read for beginning so that I can have a deeper insight in it theorically and experimentally ?

M87 Black Hole Photos and the Orientations the Angular Momentum of the Black Hole and that of the Accretion Disk. I’m trying to understand the orientations the angular momentum (let’s call it spin) of the black hole and that of the accretion disk. Veritasium has good video on the topic [1], but...

I am studying identical particles and I have some doubts. Considerer two identical spin 1/2 particles interacting through a central potential ##V##. In the rest of CM, the hamiltonian is $$ H = \frac{\textbf{P}^{2}}{2M} + \frac{\textbf{p}^{2}}{2\mu} + V(r),$$ where ##\textbf{P}## is the momentum...

If you change the spin of an entangled particle without knowing its original spin, what happens to the other entangled particle?

In http://www.feynmanlectures.caltech.edu/III_05.html#Ch5-S1, Feynman mentions that the 2-stage Stern-Gerlach experiment, which proves the electron spin states to be in a superposition, has never been actually done! I have also not seen any paper reporting such an experiment. My question is, has...

Let us for a moment look a field transformations of the type $$\phi(x)\longmapsto \exp\left(\frac{1}{2}\omega_{\mu\nu}S^{\mu\nu}\right)\phi(x),$$ where ##\omega## is anti-symmetric and ##S^{\mu\nu}## satisfy the commutation relations of the Lorentz group, namely $$\left[S_{\mu \nu}, S_{\rho...

Why do you need a weak spin orbit interactions in individual electrons in order to use the LS coupling? From what I know, we are free to combined angular momentum whenever [L1, L2]=0 and this should be true on the orbital angular momentum (and spin) of the electrons because they are...

I understand how polarization can be explained using EM waves. However, I am unable to understand how to explain how polarization filters work when we use the concept of photon spins. Can someone help me with that?

What is the difference between spin repulsion and electrostatic repulsion of an electron? Is this the same mechanism?

I'm not sure where this post belongs--here, or nuclear chemistry, quantum mechanics, NMR spectroscopy, etc. Moderator--please feel free to move it to a better location. I'm wondering if a container of liquid hydrogen subjected to a strong magnetic field would have both nuclei of each atom...

I believe that GR cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. The exchange of orbital and intrinsic angular momentum requires that the momentum tensor be non-symmetric during the exchange. GR cannot accommodate a non-symmetric momentum tensor...

Homework Statement Given the expression s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> obtain the matrix representations of s+/- for spin 1/2 in the usual basis of eigenstates of sz Homework Equations s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> S_{+} = \hbar...

I was reading the free will theorem and it basically says that subatomic particles and observers have to have free will because there's nothing prior to measurement that predetermines the outcome. Here's more: The free will theorem states: Given the axioms, if the two experimenters in question...

in this equation ##J_{ \overline{ \sigma } \sigma }^{(j)}## what are they sigma bared ? Thanks <mentor edit Latex>

i don't understand, Why The component of the total spin in the direction of H is ##M_s = \frac{1}{2}(N_{up}-N_{down})##

When learning about chirality I was very surprised to find that for QED and QCD the decay modes that would produce 2 particles with the same chirality had a Matrix Element of 0, which I took to mean that angular momentum was being conserved. Even the W only decay into RH antiparticles and LH...

i read that question and Weinberg book (A,B)-Representation of Lorentz Group: Coefficient functions of fields why u(a,b)=Cab/sqrt(2m) ? where Cab is Clebsch-Gordan coefficients, and m is mass of particle

So I was trying to see what the result for the spin precession would be if the magnetic field pointed in the y-direction instead of z. I feel like either something with what I'm doing is wrong or, I'm just overlooking something because I keep getting complex energy eigenvalues. So what I'm doing...

When a nucleus is placed inside an external magnetic field, it aligns itself parallel to the field, as that is the most stable position for it to be in. In more technical terms: it acquires an alpha spin. When you shine radio waves at this nucleus, it absorbs energy and flips over anti-parallel...

I need a 12v DC with appropriate torque. In my design, the axle of the motor would be pointed straight in the air and I want to affix a wheel to it and have the wheel spin flat, sort of like a pottery wheel sort of design. I know what the wheel is made of, its dimensions and approximate weight...

I know that spin is a type of intrinsic angular momentum. For electron spin is (1/2)ħ . But unit of (1/2)ħ is J.s, which is not the unit of angular momentum. Can you please explain this discrepancy?

Taking the Earth orbiting the sun as an example, when I consider the angular momentum of the Earth about the sun, should the spin angular momentum be counted? I'm confused that if it's counted, the spin angular momentum, Lcm=Icm×ωspin, is different from other angular momentum regarding the...

Homework Statement Prove that the Clebsch-Grodan coefficients (in the notation ##\langle j_1j_2m_1m_2|j_1j_2jm\rangle##) for the decomposition of the tensor product of spin ##l## and spin ##1/2## to spin ##l+1/2## are $$\left\langle l,\frac{1}{2},m\mp \frac{1}{2}, \pm \frac{1}{2} \Bigg\vert l...

Hi, As far as I understand spin orbit coupling is the interaction between proton of atom and electron. Proton's motion(from the frame of electron) around electron creates magnetic field. Hence electron experiences magnetic field. Does this magnetic field produces a Zeeman effect which cause...

I know that total magnetic moment of an electron (I am not sure if it is magnetic moment of electron or atom, please clarify this) is sum of magnetic moment caused by orbital motion and spin angular momentum. So, Total magnetic moment = Orbital magnetic moment + spin magnetic moment Do I have...

Suppose you have a pair of electrons in the same quantum state, and are thus spin entangled, and they absorb a pair of photons and release them at the same time. How would this affect the photons? Would the photons be entangled? Would it affect the photon spin, and if so, how would it affect the...

Hello, I don't understand how can electrons in triplet state can have the same value of spin? Shouldn't the spins be different because two fermions can't have the same state? The following picture explain my question in more detail.

I would like to ask a question about MRI Spin echo sequence. after first 90 degree RF pulse, the free induction decay occurs. And 180degree refocusing pulse is given again. And echo signal is obtained at TE. My question is that is the the signal highest when the protons are back again in...

A spin quantum number can have a value of 1/2 or -1/2. I assume that the negative means that these two spins are in opposite directions. However, what does the 1/2 mean? Why 1/2, rather than a whole integer? Are there some sort of units associated with this value?

I have a linear wire that moves let's say a distance of 1 inch. I would like this wire to spin a small gear (0.25 in circumference) 90 degrees for every 1 inch it moves. How can I accomplish this without using a bigger gear? Any ideas are appreciated. Thanks in advance

I am looking for articles or books that would clearly and succinctly state the open problem of and issues with computing hadron masses and spins in QCD from first principles, preferably in relation to the open problem of confinement and the general open problem of non-perturbative QCD. Any...

Homework Statement A beam of spin ##\frac{1}{2}## particles is prepared in the state: ##|\psi> = \frac{3}{\sqrt{34}}|+> + \frac{5i}{\sqrt{34}}|->## a) What are the possible results of a measurement of the spin component ##S_z##, and with what probabilities would they occur? b) Suppose that the...

If all three quarks in a baryon have the same flavor, they all spin the same direction, causing the baryon to have 3/2 spin. In a proton, do both up-quarks spin in the same direction (with the down-quark spinning opposite)? Or can the two up-quarks spin in opposite directions?