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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53 views

Is there magnetic dipole-dipole interaction between electrons in the quantum level?

Classically, two magnetic moments interact with each other through the magnetic field they create. Consider two electrons, the common Hamiltonian would be $$ \hat{H} = \frac{\hat{p}_1^2+\hat{p}_2^2}{...
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Antisymmetric under exchange of spins means invariant under rotation of spins?

How can I prove that this is true? I'm trying to build a BCS ground state wavefunction that is invariant under rotation of spins. The way that I wrote it is: $$u_{k}^{2}+u_{k}v_{k}\left ( c_{k,+1}^{\...
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Simple models with non-abelian anyons [closed]

It is well known, that in 1d and 2d there are particles with anyone statistics. Which 1d and 2d models have such excitations? Which model with anyons is simplest?
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Why is the $S_{z} =0$ state forbidden for photons?

If photons are spin-1 bosons, then doesn't quantum mechanics imply that the allowed values for the z-component of spin (in units of $\hbar$) are -1, 0, and 1? Why then in practice do we only use the $...
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Understanding quantum spin

I'm trying to get an idea of what spin in quantum mechanics means. I have the following questions regarding spin: The eigenvalues of the operator corresponding to the z component of spin is $\hat{S}_{...
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Spherical tensor operators relation to spin operators

I am reading a research paper discussing theoretical calculations of electron paramagnetic resonance parameters (EPR)*. In the section about higher-order EPR parameters, it states that according to ...
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How do crystals protect electronic spin qubits?

Defects in SiC crystals demonstrated entanglement between electronic spin qubits at room temperature. But do we need a crystal to protect the state? My understanding is that crystals, being uniform ...
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Calculating off-diagonal Matrix Element

Let $\vec{N}$ and $\vec{S}$ be angular momenta. The quantum number of $\vec{S}$ is $S=1/2$ while for $\vec{N}$ it is all values starting with some integer $\Lambda$ i.e. $N=\Lambda,\Lambda+1,\Lambda+2,...
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Direct measurement of $\mathbf S^2$

For concreteness, consider two spin-1/2 particles with spin vectors $\mathbf S_i=(S_i^x,S_i^y, S_i^z)$. The total Hilbertspace is four-dimensional, and as a basis we can take the (simultaneous) ...
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Spin state rotations and spinors rotations

I've tried to do the calculations to derive the SU(2) matrices that rotates spinors from the rotation of the spin eigenstates. The following is the procedure that I followed but at the end I didn't ...
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Fermion operators: why $\rm SU(2)$ symmetry and not $\rm U(2)$ symmetry?

Let us consider operators $c_{\uparrow}$ and $c_{\downarrow}$ which destroy a fermion with spin up and a fermion with spin down, respectively. These operators can be found, for example, in the Hubbard ...
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What is the use of $g$-factor for magnetic moment of electron?

$g$-factor is also called the spectroscopic splitting factor according to "Introduction to Solid State Physics" by Charles Kittel. So it can be presumed that it is related to the splitting of levels ...
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Measuring electron spin with multiple Stern–Gerlach apparatus at an angle

To separate the two spins of electron of a particular direction, we use Stern-Gerlach apparatuses to apply a non-uniform Magnetic field. Suppose we have two identical electrons and we know their spin ...
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Components of Stern-Gerlach Filter

Came across a discussion of the EPR paradox and Bell's inequality in a psychology text. I started looking deeper into the Stern-Gerlach type experiments employed in the EPR discussion and found this ...
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Spin-Spin interaction

In Herzberg I (p.223) are formulas for the rotational spin-splitting of a $^3\Sigma$-state in Hund's case (b). In this case the electronic angular momentum is coupled to the internuclear axis (z-axis) ...
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Why Pauli called the swap matrix $σ_x$? Why not $σ_y$?

Why Pauli called the following matrix $\:\sigma_x\:$ and not $\:\sigma_y$? \begin{equation} \sigma_x\boldsymbol{=} \begin{bmatrix} 0 & 1 \vphantom{\tfrac{a}{b}}\\ 1 & 0 \vphantom{\tfrac{a}{b}}...
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Stern-Gerlach experiment with a magnetic field inbetween

An experiment is set up so that a beam of spin-1/2 is prepared for $S_{z} = \hbar/2$, it then passes a constant magnetic field $\textbf{B} = B_{0}\textbf{e}_{x}$ with the velcity $v_{0}$ for a ...
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If $s_1$ has spin up and $s_2$ has spin down how to find $s_1.s_2 $? what state should i take for coupled $s$ whether singlet or triplet?

Two spin half particle one up spin one down spin how to calculate $s_1\cdot s_2$? what state should I take triplet or singlet? while we don't encounter the problem in two spin up particle
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Why is the graviton spin supposed to be 2, and how can it interact with matter? [duplicate]

As far as I know, gravitons are predicted to be spin-2 particles because some extrapolation from GR about non-linearity and antisymmetry. I think I want some clarification on that. What are some ...
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Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
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How does electrostatic repulsion between electrons in “many electron atom” lead to coupling of individual orbital angular momentum vectors?

I just started studying $LS$ coupling scheme, book has described $LS$ coupling in following order  1. Firstly it mentions due to "spin-spin" correlation individual spin angular momentum vectors ...
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Electric dipole moment (EDM) and CP violation

It's well known that a non-zero value for the electric dipole moment (EDM) would imply CP violation. If we consider the interaction Hamiltonian of an EDM $d$ with an electric field $\vec{E}$, $$ H = -...
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Does spin angular momentum change with reference frame?

I am guessing that the angular momentum of a particle measured by different inertial observers (no gravity) is different. At the same time, since quantum spin is an intrinsic property, Is it true ...
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What is Residual Electrostatic Interaction and how does it leads to $L$-$S$ coupling?

The answer to this question I have is that, in Hartree's self consistent field for calculating potentials and solving out Schrodinger's equation, we consider that if the system has $N$ electrons than $...
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If the electron have spin 1 , how many electrons would be required to fill 1s orbital? [closed]

How many electrons can be filled in 1s orbital, if electron have spin 1 instead of 1/2.
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What is polarisation, spin, helicity, chirality and parity?

Polarisation, spin, helicity, chirality and parity keep confusing me. They seem to be related, but exactly how they are related is unclear to me. Can someone maybe give a short overview about what ...
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Spin pumping: interface between a Ferromagnetic and a normal metal

We know that at the interface $(y=0^+)$ of a ferromagnetic material (FM) with excited magnons, and a normal metal (NM), there is an injection of spin current (or spin pumping) arising from the magnons ...
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Orientation of superposition of two spins

I was reading this paper. The paper states that $$d_x(|\uparrow\uparrow\rangle+|\downarrow\downarrow\rangle)+id_y(|\uparrow\uparrow\rangle-|\downarrow\downarrow\rangle)+d_z(|\uparrow\downarrow\rangle+|...
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Are there two different spinors for the same spin state?

Let's say $ \begin{bmatrix} 1\\ 0\\ \end{bmatrix} $ and $ \begin{bmatrix} 0\\ 1\\ \end{bmatrix} $ are the eigenvector of $\hat S_z$, is the state $ -1\begin{bmatrix} 1\\ 0\\ \end{bmatrix} +0\begin{...
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How to produce a given entangled state of two quantum bits?

I was watching Leonard Susskind's video series on quantum entanglement, where he looks at the spins of two electrons. In particular, there are entangled states of the form $$\alpha\left|\uparrow \...
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How to calculate probabilities of eigenvalue of observable with multiple eigenvectors (degeneracy)

I was calculating the probability that for a two spin system, prepared in a state $\mid rr \rangle$ (which can be expressed as a combination of basis vectors $\mid u \rangle$ and $\mid d \rangle$), a ...
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Hamiltonian matrix elements involving ladder operators for spin-1 state

I am reading the Doctorate thesis 'Zero-Field Anisotropic Spin Hamiltonians in First-Row Transition Metal Complexes: Theory, Models and Applications' (link: https://tel.archives-ouvertes.fr/tel-...
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Would a spinning particle in a spinning universe have spin? [duplicate]

Imagine a massless left-handed neutrino travelling along the x-axis with angular momentum 1/2. Now change to a reference frame of a rotating universe on the same axis. Someone in this reference ...
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Angular momentum of a single particle

I have to answer the following question: Consider the decay $\rho^0\to\pi^+\pi^-$. The rho meson has angular momentum 1, what must the orbital angular momenta of the pions be, given that they are ...
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Good Quantum numbers in $L$-$S$ coupling

I'm having a hard time understanding a few things about L-S and j-j coupling in 2 (or more) electron atoms. What I picked up from our lectures is the following: The Hamiltonian can be "broken up" ...
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What is the direction of spin in the Fourier transformed space for the following situation?

I have an expression, like, $$\frac{1}{2}\mathbf{\hat{q}}\cdot\xi^{r\dagger}\boldsymbol{\sigma}\xi^s,$$ where, $\mathbf{\hat{q}}$ is the momentum unit vector and $\xi^s$ is a Dirac spinor. The above ...
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Confusion about Stern-Gerlach experiment

Why does the particle always have the same spin magnitude $\pm \frac{1}{2}\hbar$? In classical mechanics we can split a vector into components but in quantum mechanics due to uncertainty principle ...
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1answer
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Find the wave functions of 2 identical particles in infinite square well given their spin

I want to find the wave functions for the three first energy states of 2 identical particles in an infinite square well for two cases of spin 1) both have zero spin 2) both have 1/2 spin I know ...
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Hydrogen relativistic energy levels: Why is this operator equivalent to this matrix?

I am trying to understand the derivation of the relativistic energy levels for the Hydrogen following the annex 2.2 of this notes. Until the equation below I could follow the reasoning: $$\left [-\...
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Total spin on a two particle system

How can I know the total spin of a given state quickly? I first encountered this problem when proving the Clebsch-Gordan series. Consider a two particle system (to make it easier, lets say identical ...
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Spin of skyrmion

Baryons can be considered as solitions in Skyrme model(See also this post.): Such Lagrangian haven't any information about number of colors. Bosonic or fermionic nature of baryons depends on number ...
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How exactly does an electrons spin cause it to have a magnetic moment?

So I understand you can rearrange the equation for a single electron orbiting in a circle $(\mu=evr/2)$ and substitute in the associated velocity for angular momentum $(v=L/mr)$ where angular momentum ...
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Is it possible for an electron in the atom to spontaneously change the direction of its spin component on the z-axis?

By "spontaneously" I mean without interacting with any external field. More specifically, can the $S_z$ component of an electron's spin collapse into one of its two possible states ($S_{z\pm} = \pm\...
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How can we get this identity?

I would like to know how we can get this identity: $$\vec{S}_1·\vec{S}_2 = S_1^zS_2^z + \frac{1}{2}(S_1^+S_2^-+S_1^-S_2^+).$$ The $S_1, S_2$ is the spin operator of the electrons, 1 and 2, and $S^+, ...
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Physical description of spin wave theory and Bogoliubov transformation

I am trying to understand how spin-wave theory explain the behaviour of a spin-wave in a spin system. To clarify my question, I will start with a simple case of a antiferromagnet (AFM). The ...
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Why must the ground state of helium be a singlet?

Every reference I have seen, including e.g. question (a) on page 5 of these notes or the comments in the answer of this post, use a hand-wavy perturbation theory argument for non-degeneracy of the ...
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Hamiltonian for the spin-orbit coupling in spinor-notation

After some research I can't find a good source which explains how to write the Hamiltonian of a spin-orbit coupling in spinor notation. The following notation is commonly used $\hat H =\xi \hat L.\...
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1answer
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Eigenvalues of a two particle system in a coupled vs. uncoupled basis

Consider a system of two distinguishable spin-1/2 particles with Hamiltonian \begin{align} H &= \frac{\alpha}{4} \vec{\sigma}_1 \cdot\vec{\sigma}_2.\\ \end{align} where $\vec{\sigma}_1 = (\sigma_x\...
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2answers
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Is $\boldsymbol{\nabla}\cdot\mathbf{S}$ zero?

There exists a classical definition of the orbital angular momentum, $$\mathbf{L}=\mathbf{r}\times\mathbf{p}$$ Due to this definition, the following quantity is identically zero, $$\boldsymbol{\nabla}\...
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Spinful time reversal and SOC

I'm having some trouble with understanding the distinction between spinful and spinless time-reversal in a real materials context. 1) Does spinful time-reversal (e.g. $\mathcal{T}^2 = -1$) imply spin-...

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