Spin Definition and 1000 Threads

I believe I understand the mathematical derivation of the Dirac equation. I understand how the four 4X4 matrices, and their relation to the 2X2 Pauli Matrices, arise from that derivation. I understand that the 3 spin observables for Fermions are ALSO represented by the 3 Pauli Matrices...

Hi, Assume I’m solving a 2-particle (fermions) problem in a potential well. If I set the wavefunction as anti-symmetric, then by default I’m assuming that the two particles has the same spin and hence exchange interaction has to be accommodated for. But what if the 2 fermions have different...

The spin 4-vector is defined in the rest frame of the particle as s^{\mu}= (0, \vec{s}). Why is the zeroth component of the same zero in this frame?

As we know photon's helicity are \pm1. Helicity is the projection of the spin S onto the direction of momentum, p, which is considered as Sz. What about Sx and Sy? They are both ZERO?

"Locally, the spin density S is an intrinsic (i.e. origin-independent) quantity, which is associated with the local ellipticity of the polarization of light. In turn, the orbital AM density L=r x P0 is a manifestly extrinsic (origin-dependent) and is produced by the corresponding canonical...

If a fast moving and heavy object strikes earth,can it change its spin or rotation or both?

i mean, people are creating LHC to split the atoms, but why don't we just spin it? spin in in high speed and see if a quark/photon/electron would break can we not do that? is it mathematically impossible to have a mass in the center of rotation?

I'm trying to get my head around this spin idea, the idea that particles behave like tiny dipole magnets when passing through a magnet field, either spin up or spin down. Because unlike magnets they don't produce a spread on at the end, they are either top or bottom. So the problem I have...

So I've just been reading about the Stern-Gerlach apparatus/experiment and had some questions about the half spin probabilities... First let's say a collection of spin-half particles are sent through a S-G apparatus (which I know measures the z component of particles spin angular momentum)...

To define spinors in QM, we consider the projective representations of SO(n) that lift to linear representations of the double cover Spin(n). Why don't we consider projective representations of Spin?

Trying to get my head around this one. Given that you can have a proton and an electron in a hydrogen atom for example, and they can create a singlet or triplet configuration, with spin 1 and spin 0 respectively. The total spin operator can be derived as: S^2 = (Se + Sp)^2 = Se^2 + Sp^2 +...

Homework Statement The interaction between the spins of the two particles in a hydrogenic atom can be described by the interaction Hamiltonian $$\hat{H_I} = A \hat{S_1} \cdot \hat{S_2}.$$ Compute the splitting of the ground state due to ##\hat{H_I}##. Both particles have spin 1/2. Homework...

Number of Spin "s" States Homework Statement For a system of two identical particles with spin s, determine the number of symmetric and anti-symmetric spin states. 2. The attempt at a solution This does not seem like a problem that is that difficult, but I am having some trouble...

Hello Everyone, General curiosity question. We start with a particle who is in superposition. We observe it and collapse its wave function. This is how the particle's spin is determined. Two states can exist, spin up or spin down. My question is, once we observe the spin state, is...

A spin 1/2 particle A undergoes decay A→B+C+D Where it is known that B and C are also spin 1/2. The complete set of allowed values of spin of D It was a Multiple Choice Question and options given were 1) 1/2,1,3/2,2,5/2,3,... 2) 0,1 3) 1/2 only 4) 1/2,3/2,5/2,7/2,... I tried the...

Spin Foam Gravity (SFG) has reached a stage of development where perhaps we could have a new abbreviation to distinguish it from previous Loop gravity formulations. I could be wrong about this, of course, but I want to see how things look from that angle. There seem to be some...

Homework Statement Homework Equations The Attempt at a Solution Angular momentum is the only parameter conserved. This is because there are no external torques acting on the system. Energy is not conserved because the collision is inelastic. Finally, linear momentum is not...

Spin is an operator with components (Sx,Sy,Sz) but do these represent "spatial" components. The question arose because the spin of an electron sets up an angular momentum L = -e/m * S (S and L are vectors) So inverting the spatial coordinate system and requiring that the physical result must...

Hi, I have a few questions regarding the experimental outcome of the stern-gerlach experiment. Let's suppose the following setup: We have a magnetic field whose field-lines point towards the positive z axis and the intensity of that field becomes stronger towards the positive z axis, so there...

I am currently confused... I read that we don't know yet where does the proton spin come from. But I wonder... 1) Doesn't the proton have effectively 3 quarks of spin 1/2 (I said effectively to leave out the quark-gluon sea within the proton)? In that case, 3 spin 1/2 particles can't be added...

The 3s and 3p orbitals are filled by 4 electrons.A single atom has [Ne]3s2 3p2.But when multiple atoms get together they do so in order to minimize the overall energy.And to minimize the overall energy,the 3s and 3p orbitals hybridize to form 4 tetrahedral SP3 orbitals.And the Si atoms get...

We say that spin is an intrinsic angular momentum which does not have anything to do with space. But is it possible that it is the orbital angular momentum of some internal constituent particles (a yet unknown fine structure)?

Homework Statement Consider a system of two spin 1/2 particles, labeled 1 and 2. The Pauli spin matrices associated with each particle may then be written as \vec{\hat{\sigma _{1}}} , \vec{\hat{\sigma _{2}}} a)Prove that the operator \hat{A]}\equiv \vec{\hat{\sigma _{1}}}\cdot...

When a electron or any charge spins what is the direction of the magnetic field generated by its spin? what is the rule connecting the direction of spin of the charge and direction of magnetic field

does nucleus in an atom spin?

I thought this was cool, wasn't able to find a paper on it, but didn't look "super hard", and won't pay for it. Apparently, a gravitational lensing has lined up so perfectly that we were able to measure the black hole's spin. They have it at "half the speed of light" (??!)...

hello guys , in this problem from zettili quantum mechanics that i attach , i think something is wrong , first the problem said two particles with spin 1/2 but didn't mention that the system is in singlet state or triplet state , so if the system be in triplet state then our spatial wave...

Spin-1 matrix Sx, Sy, Sz are traceless 3*3 matrix, and have the property ##[S_i, S_j] = i\epsilon_{ijk}S_k##, and we know that ##Tr(S_i^2) = 1^2+0^2+(-1)^2=2##. All of the above are independent of representation, of course, the trace of a matrix is representation-independent. so, if we want...

Homework Statement For a spin 1/2 system, the eigenstates of z-component of the angular-momentum operator Sz are given by: S_z |\pm> = \pm \frac{\hbar}{2}|\pm> Suppose at time t, the state of the system is given by: |\psi> = a|+> + b|-> If Sz is measured, what are the possible results of...

Question about quantum spin: So for the Schrodinger equation, the angular momentum of a wave-packet, whether it is free or confined to a potential well, appears to be calculated in exactly the manner you would expect it to be: L(x) = m*rxv[Psi(x)]. Aside from quantization (decomposing the...

Hi everybody, In most classical or quantum optics texts an angular momentum is considered for the EM radiation as the following: J = ε_0 ∫_V r × [E(r, t) × B(r, t)] d^3 r Then it is claimed that: "Using the usual formula for a double vector product and integrating by parts...

Hi, this probably has been answered somewhere here already, but I was unable to find it. Could someone explain how the spin of a particle is actually measured in an experiment ? Most interesting to me is how the 3d spin vector for 1/2 spin particles is determined experimentally. Cheers.

The spin angular momentum of a spin 1/2 particle is given by S = √(s(s+1))ℏ. If s =1/2, S= ((√3)/2)ℏ So, if s=1 is S= √2ℏ ?

The epr paradox is usually explained as something like: Suppose you have two electrons in the singlet state (+=spin up, -=spin down): lψ>= l+>l-> - l->l+> Now if you measure the spin on the first electron the explanation is (I think) that this collapses one electron onto l+> or l-> such...

Hi PF members. I have got a little worry I am familiar with the Zeeman term that always appears in the Hamiltonian of a spin chain representing the influence of an external magnetic field. I don't know if there is a similar term if the spin was rather in he presence of an electric field ( I...

I am reading a text about the splitting of the energy levels in crystals caused by the spin orbit interaction. In particular, the argument is treated from the point of view of the group theory. The text starts saying that a representation (TxD) for the double group can be obtained from the...

Homework Statement An alkali atom, on it's fundamental state, passes through a Stern-Gerlach apparatum, which will only transmit atoms with their spins aligned along the +z direction. After that the atoms travel, during a finite time τ, through a region of constant magnetic field...

So I know this might be a lot to read but I am having a very hard time understanding how to use the formulas in degenerate perturbation theory. Here is the problem I am on. Homework Statement A system of two spin-1/2 particles is described by the following Hamiltonian...

quantum spin vs ...spin I keep hearing people say, "comparing particle spin to a spinning top will lead you in the wrong direction." I'm curious.. what exactly is the difference between the two?

What is the link between the polarisation of light and photon spin?

In my textbook there is an equation for the precession frequency: Ω = τ/Iω The derivation in the book shows no difference in the spin angular momentum at time t = 0 and t = delta t but when I tried it I got that the denominator of the above equation must be the 'new' angular momentum (at t...

Hi, please could someone provide me with an explanation of the differences between the magnetic quantum number and the spin. I thought that the magnetism of an electron/fermion comes from its intrinsic quantum angular momentum (i.e. its quantum spin) which was evidenced by the Stern–Gerlach...

Homework Statement Consider an electron with spin \frac{1}{2} and orbital angular momentum l=1. Write down all possible total angular momentum states as a combination of the product states | l=1 , m_l > | s = \frac{1}{2} , m_s > Homework Equations Lowering operator : J_- |j, m> =...

Hi, please could someone explain the notion that particles of 1/2 integer spin do not look the same when turned through 360 degrees. This notion seems to crop up when I read around QM but nobody seems to explain how this came about. So my question is this - what experiment shows/confirms that...

Suppose we consider the spin 1/2 measurement matrices B=\frac{1}{\sqrt{2}}\left(\begin{array}{cc} 1 & 1\\1&-1\end{array}\right) and A=diag(1,-1) it's easy to show that B^2=A and a normalized eigenstate of B |\Psi\rangle=\left(\begin{array}{c}a\\b\end{array}\right) with eigenvalue 1 ...

What is the Lagrangian of interaction of photon and spin zero charge scalar?The vertex of photon and spin 1/2 charge fermion is proportional with e multiplied vertor gamma matrix,but I do not know what is the vertex of photon and charge scalar.I hear that a vertex is proportional with polynomial...

Dear members, I'd like to collect those properties of "spin" that makes it different to a normal (classical) angular momentum or magnetic moment. Please help me, correct, reword my sentences one by one. I'd like to create a short but still understandable and correct list. 1. Spin quantum...

how actually electron and protons spin? explain me whether this spinning could provide torque to the positive charges then it means electrons and protons keeps rotating under their electrostatic field?

i am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and neutrons separately, I found 3 protons in the 1d5/2 sub-shell and 4 neutrons in the same 1d5/2...

Recently, I was thinking about spin and isospin. It's been a while since I've dealt with particle physics, so my knowledge may be a bit rusty. In the Standard Model, we have three interactions with associated coupling constants e, gw and gs. A particle may have three different charges Qe, Qw...