Questions tagged [quantum-spin]

Fundamental characteristic property of particles which together with orbital angular momentum acts as the generator of rotations and which doesn't have a classical equivalent but is sometimes compared to and contrasted with classical intrinsic angular momentum.

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1answer
52 views

Why does Hamiltonian no longer commutes with $\mathbf L$ and $\mathbf S$ in presence of spin orbit coupling?

Is this something due to change in Hamiltonian due to relativistic correction. i.e. $H$ being $$(\frac{e^2}{4\pi {\epsilon _0}}) \mathbf{S \cdot L}$$ instead of $$(\frac{e^2}{8\pi {\epsilon _0}}) \...
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Correct Visualization of a Spin Wave in a Ferromagnetic material

One way of describe a ferromagnetic material is the Heisenberg hamiltonian $ H = -\frac{J}{2} \sum_{<i,j>} $S$_i$S$_j$ where $J$ measures the interaction between spins (positive for ...
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I want know that all up and down spin of particles have same angular momentum

Do all free electrons have the same angular momentum?
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Can nuclear spin interactions drive nuclear transitions?

The atomic nucleus is often treated as monolithic from the perspective of atoms and molecules, but NMR demonstrates that nuclear states can be affected through external means. Especially the ...
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Is there an easy way to compute $\exp(-i\pi J_2) |jm\rangle = (-1)^{j-m} |j,-m\rangle$?

Is there an algebraic way to compute $\exp(-i\pi J_2) |jm\rangle = (-1)^{j-m} |j,-m\rangle$. I know this is basically the Wigner $d$-matrix (which I can just look up), but how is it derived in this ...
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Physical interpretation of triplet state

When we look at a triplet state we know its spin part $\sigma(1,2)$ must be symmetric. Then it must be proportional to: $\sigma_{\uparrow}(1)\sigma_{\uparrow}(2)$ $\sigma_{\downarrow}(1)\sigma_{\...
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Optimal measurement for distinguishing states

Suppose we have $n$ identical spin-1/2 particles prepared by some machine. Depending on the setting of the machine, either all the particles are in state |$z_+$> or they are all in state |$x_+$ > (...
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Is spin-orbit coupling mass dependent?

When comparing spin-orbit coupling in the case of electrons and in the case of nucleons, do nuclear states exhibit a stronger level splitting compared to atomic states because the nucleons are more ...
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What are differences among chiral, helical and spiral in quantum spin context?

For chiral, as far as I know, there are vector chirality $\kappa_{ij}=\mathbf{S}_{i}\times \mathbf{S}_{j}$ which characterizes non-collinear spin arrangement and scalar chirality $\chi_{ijk}=\mathbf{S}...
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Will a particle's spin evolve abruptly if the magnetic field it's in changed abrubptly?

If a particle (say electron) was placed in a magnetic field with only a z-component ( $B_0 \hat{k}$ ), then according to the equations $$H = - \mu \ .B \ \ \ \quad \quad \quad \quad\mu =\gamma S $$ ...
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How can one calculate spin polarizations for molecules?

it may be a simple question but I'm having trouble in this topic. For example, How can I calculate spin polarization values of molecules such as $CO$, $H_2$, $BeH$, $CsH$, etc.
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In addition of angular momenta of two half spin particles, when we try to find square of the total momenta where do some components go?

Reference :- Page 189 Griffiths's Introduction To Quantum Mechanics He supposes the momenta of two particles to be $S^{(1)}$ and $ S^{(2)}$ The Spin Momenta $S^{(1)}$ get vector components as $S^{(...
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Doesn't spin-spin interactions in gravity disobey Galilean relativity?

In gravity (GR) apparently there are forces which occur which are related to the spin of two masses. For example if we had a rotating gravitational source and dropped, say, some particles into it ...
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Hamiltonian invariant under rotation of spins

Two spin half particles interact via the Hamiltonian $$H=J \vec{S}_{1}\cdot\vec{S}_{2}$$ It is said that this Hamiltonian is invariant under uniform rotation of spins. I don't see how this is ...
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Is a 3-terminal magnetic tunnel junction possible?

I am wondering, whether a 3 terminals magnetic tunnel junction can be implemented, as shown in the figure below. At the bottom I have a normal metal (NM), on the top - a magnetic junction (FM = ...
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Equilibrium density matrix for a homonuclear spin system in NMR

I'm currently reading this paper. In the paragraph under fig. 3 on page 2, they write: The equilibrium density matrix for a homonuclear spin system is a sum of $n=5$ terms: $IIIIZ+IIIZI+IIZII+IZIII+...
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How does an isolated electron in deep space 'know' it is spinning? [duplicate]

This is a question about Mach's principle. Why is Mach's principle still an open question? In particular, if inertia arises from distant matter, Mach's principle raises the question would a particle ...
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1answer
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Did the Feynman heuristic of “simple effects have simple causes” fail for spin statistics?

Someone here recently noted that "The spin-statistics thing isn't a problem, it is a theorem (a demonstrably valid proposition), and it shouldn't be addressed, it should be understood and celebrated." ...
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Is it not necessary for electrons to move to create a magnetic field?

We have been taught about diamagnetism and paramagnetism on basis of the bohr's atomic model in our school. However, we know that electrons actually do not go in complete circles or tracks, they exist ...
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Does spin $0$ violate the uncertainty principle?

It seems that if we have some spin eigenstate $|0\rangle$ for which the square of the total spin operator is $\hat{S}^2|0\rangle = 0$, then we simultaneously know the spin in all three directions, ...
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Kinematics of Spin

By generalizing $n$ component wave function in three dimensions, Under an infinitesimal rotation around z-axis,the wave function is transformed as follows: $$\left[ \begin{array}[c] \psi \psi'_1 \\ \...
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1D linear spin-chain for Ising model

In section 2.1 of the article https://arxiv.org/abs/1807.07112 appears the following Hamiltonian for a 1D chain of $n$-spins $$ H = \sum_{i = 1}^n \sigma^x_i\sigma^x_{i + 1} + \sigma^y_1\sigma^z_2···\...
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How can there be nuclear spin-orbit interactions with only neutral and positively charged particles in the nucleus?

At the atomic level, spin-orbit interaction is motivated by the magnetic field experienced by the negatively charged electron orbiting the positively charged nucleus. However, at the nuclear level, ...
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When exactly are protons attracted to other protons and neutrons?

When proton and proton neutron and neutron proton and neutron are attracted to each other or repelled from each other in terms of strong interaction (ignoring electromagnetic interaction)? I read ...
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What does this notation for spin mean? $\mathbf{\frac 1 2}\otimes\mathbf{\frac 1 2}=\mathbf{1}\oplus\mathbf 0$

In my quantum mechanics courses I have come across this notation many times: $$\mathbf{\frac 1 2}\otimes\mathbf{\frac 1 2}=\mathbf{1}\oplus\mathbf 0$$ but I feel like I've never fully understood what ...
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Does a quadrupole transition mean emission of one photon with spin 2?

If it's true and spin-2 photons do exist, could you please point to some literature that discusses spin-2 photons? If not, then how exactly does a selection rule for quadrupole transition make sense ...
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How to derive the general expression for eigenvalue for the square of Pauli Lubanski operator?

After some trials, I managed to get the correct eingenvalue $(\frac{-3}{4}m^2)$ for $W^2$, where $W$ is the Pauli Lubanski pseudo vector. The expression for each $J^{\mu \nu}$ is a sum of a 4x4 ...
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In a subatomic particle the particles spin [closed]

In a subatomic particle the particles spin on their axes as well as they rotate around the nucleus. But the question is what is the direction of rotation when viewed from one point? Is it clockwise or ...
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Confusion about expected outcomes of Stern-Gerlach Experiment

First of all, I know there are similar related questions but there is something that bothers me. We can relate the magnetic moment and angular momentum as $\vec{\mu} = \gamma \vec{l}$ (1) So in ...
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1answer
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Intuition of spin of photon [closed]

I read that intrinsic spin is a quantum property aka just a number, charged particle such as electron has magnetic dipole moment which can be detected using magnetic field like the Stern–Gerlach ...
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Reference regarding classical treatment of spin

While going through these notes about spin, I encountered the classical Lagrangian for spin (section 2). But the treatment here is very concise and I can't seem to find any other resources treating ...
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Optical lattices - spin

I know different potentials can be realised with spin dependent optical lattices. My question is, how do the optical lattices become spin dependent? I cannot find a good explanation on the literature,...
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Ising model Monte Carlo simulations in 4D and 5D

I'm going to be simulating the Ising Model in 4D and above to calculate spin-spin correlations and critical exponents and am wondering how to tackle this algorithmically. For example, in 1D, use an ...
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Electrons on Stern–Gerlach experiment

My questions about spin and negative charge of electrons. Stern-Gerlach experiment is very famous in order to find spin of electron. this video created by paris-sud university really well-explained on ...
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Unpolarized $e^+e^-\rightarrow\mu^+\mu^-$ scattering

On Schwartz’s QFT book, page 232, it’s calculating the cross section for $e^+e^-\rightarrow\mu^+\mu^-$ scattering, assuming spin and polarization are not measured, and it writes Let us also assume ...
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Write the spectral decomposition of the spin angular momentum operators using the Dirac braket notation

Could someone show me how to write the spectral decomposition of the $x$ and $z$ - components of the spin angular momentum operators $S_x$ and $S_z$ using Dirac Braket notation and how to express this ...
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Why is the singlet state for two spin 1/2 particles anti-symmetric?

For two spin 1/2 particles I understand that the triplet states ($S = 1$) are: $\newcommand\ket[1]{\left|{#1}\right>} \newcommand\up\uparrow \newcommand\dn\downarrow \newcommand\lf\leftarrow \...
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Madelung equation for particle with spin

I have looked at the Madelung representation of quantum states and found it interesting, but when I tried to derive an analogous theory for particles with spin 1/2, I ran into troubles with spin orbit ...
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Physical explanation of spin-orbit interaction in many-electron atoms & nuclei

The electron of a hydrogen atom or any hydrogenic ion sees an internal magnetic field $\vec{B}_{\rm int}$ due to the proton or the nucleus in relative motion w.r.t the electron. The spin magnetic ...
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1answer
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Spin operator in tight-binding model

While reading Altland and Simons (Condensed Matter Field Theroy, p. 60), I came across the following problem. In tight-binding models, the exchange interaction contributes to the Hamiltonian in a form ...
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Two spin 1/2 particles and measurement of their spins

Let's say I have two spin $\frac{1}{2}$ particles in a singlet state. I measure the y-spin of the first particle and find it to be $+\frac{\hbar}{2}$. Then how do I calculate the probability that upon ...
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1answer
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Is it known if the ground state of an arbitrary electronic many-body problem has antisymmetric spatial part?

For non-interacting electrons, Hund's rule (#1) says that the state with the highest total spin has the lowest total energy. For two independent electrons, it seems then that the electrons should be ...
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Spin operators in QM

In a text (Introduction to Quantum Mechanics by Griffiths) I am using it states without motivation that spin angular momentum has the same commutations relations as orbital angular momentum (these ...
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Where is the information for a particle's spin stored? [closed]

I understand that spin is an intrinsic property of certain quantum particles, and that it’s just an analogy to classical spin, but that’s not really what I’m asking. Spin is often described as being "...
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1answer
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Arriving at the $\big(\pi_\ell,P_\ell(\mathbb{C}^2)\big)$ representation of $\mathfrak{su}(2)$

I think I'm really close, but confused on applying the multivariable chain rule and untangling the result. The $(\Pi_\ell,P_\ell(\mathbb{C}^2))$ representation of $SU(2)$ induced from the fundamental ...
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1answer
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Second order relativistic corrections to Pauli equation from Dirac equation

I'm trying to derive the full and correct Hamiltonian for spin$\frac{1}{2}$ particles from Dirac equation up to second order in $v/c$. For a potential and magnetic field constant in time. In ...
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Rotation generators calculation $(J^{\pm})^2=s_{\pm}(s_{\pm}+1)$ [duplicate]

The generators of the Lorentz group $M_{\mu\nu}=-M_{\nu\mu}$ can be split into $$ M_{ij}=\epsilon_{ijk}J_k $$ and $$ M_{0i}=K_i $$ rotations and boosts respectively. These obey the commutation ...
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Why are $SU(2)$-generators interpreted as *spatial* components of spin?

The generators of the unitary representation of $SU(2)$ on the internal spin Hilbert space of (say) a spin-$1/2$-particle are typically said to represent components of spin along various spatial axes. ...
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1answer
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Measurement of quark's spin

Since quarks always form bound states, how do we know the spin of a single quark is $\frac{1}{2}$ experimentally?
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852 views

Position representation of spin states and spin operators

How can we represent a spin states $ \lvert S_x:+\rangle, \lvert S_y:+\rangle,\lvert S_z:+\rangle ,\lvert S_x:-\rangle, \lvert S_y:-\rangle $ and $\lvert S_z:-\rangle$ in position representation ...

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