Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

3
votes
2answers
36 views

Why can we factorize the state of a particle?

I read about factorization in this two cases. First, since spin is not coupled with position and time it is possible to factorize the state in a spinor and a wave function. Second, in the 2 particles ...
0
votes
1answer
32 views

Relation between quantum numbers $j$ and $\ell$

I'm given the following problem: "Consider an atom with orbital angular momentum $l$. What are the possible values of the total angular momentum quantum number $j$? Treat the case of $\ell = 0$ ...
2
votes
4answers
49 views

Interpretation of rotating a quantum state

I'm currently taking an introductory quantum mechanics course, where the last covered topic was spin and identical particles. During some reading online, I stumbled across the term "rotating a quantum ...
0
votes
0answers
19 views

Determining the probability of measuring spin state

I am having some problems figuring out the following question regarding probabilities of spin states. The Question Consider the spinor $$|\psi\rangle=\frac{1}{\sqrt{5}} \begin{bmatrix}2 \\ 1 \end{...
0
votes
1answer
20 views

How do the vector and scalar potentials transform under electromagnetic duality trnasfotmation?

Maxwell equations are invariant under the duality transformation. The electric and magnetic fields are defined in terms of these potentials. How do these potentials transform under duality?
-3
votes
1answer
41 views

Gauge Invariance of Spin Angular Momentum of EM waves [closed]

How can I prove, the Spin Angular Momentum of Electromagnetic Wave to be not Gauge Invariant?
1
vote
1answer
43 views

Does total $\hat{S}^2$ always commute with total $\hat{S}_z$ even for interacting spins?

I was given the following operator $\hat{f}$ describing the interaction of two spin-$\frac12$ particles: $$\hat{f}=a+b{\hat{\bf S}_1}\cdot{\hat{\bf S}_2}.$$ I was told that I can prove that $\hat{f}$...
0
votes
1answer
31 views

Calculating the spin given the baryon wave function

This is probably a trivial question and I am missing something conceptually simple here. I have the spin part of the total wave function of a baryon consisting of three light quarks: \begin{equation}...
0
votes
3answers
78 views

Why is the proton (uud) lighter than the $Δ^0$ (uud) baryon?

Neutron has quark composition udd with spin $\frac 12$. $\Delta^0$ baryon has quark composition udd with spin $3 \over 2$. On Wikipedia it says that $\Delta$ baryons have mass of approximately $1232 ...
1
vote
1answer
45 views

Two spin-1 system and the projector onto total spin 2 subspace

I am having trouble grasping the projection operators in the context of composite spins system, e.g. with two spin-1. First off, a projector $P$ is said to be an operator that squares to itself, $P^2=...
0
votes
0answers
34 views

Which atom numbers are possible with three bound states?

According to the Pauli principle, which atomic numbers are possible given three bound states? I know what the Pauli principle says, but I don't know how to go about finding the atomic numbers. I'm ...
2
votes
2answers
33 views

Different global phase shifts of Pauli-$z$ Matrix eigenstates from rotations around $z$-axis

I understand the pauli matrix $\sigma_z = \bigl( \begin{smallmatrix}1 & 0\\ 0 & -1\end{smallmatrix}\bigr)$ rotates a state around $z$-axis by angle $\pi$ in $SO(3)$. We can see it works by ...
1
vote
1answer
44 views

Is there a QM measurement that can distinguish spin in up orientation and in left orientation?

Alice creates an electron with its spin |up> or |left>. If Bob measures the spin with an (up_or_down) operator he might get result ...
0
votes
2answers
64 views

What elementary particles have properties that vary by spin direction?

This table of elementary particles indicates that electron spin = 1/2. My understanding is that electron spin may proceed in two directions which may be denoted by spin sign and that electron spin ...
1
vote
3answers
78 views

Can an atom be split and put back together? [duplicate]

I had recent came across this question when unintentionally tearing a piece of my journal paper. These atoms' bonds are pulled apart when the paper is torn, but is there a way to put them back ...
1
vote
1answer
66 views

Why do spinning electrons generate magnetic dipole moments?

Can the spin of electrons generate currents? If not, how does it create magnetic dipole moments?
0
votes
2answers
48 views

$j=\frac{1}{2}$ addition of angular momentum

For $j=\frac{1}{2}, j'=\frac{1}{2}$ we have $$|11\rangle=|\frac{1}{2}\frac{1}{2}\rangle$$ $$|10\rangle=\frac{1}{\sqrt{2}}(|-\frac{1}{2}\frac{1}{2}\rangle+ |\frac{1}{2}-\frac{1}{2}\rangle)$$ $$|10\...
-1
votes
0answers
44 views

Why do we say we need a complex number to describe a quantum property (say spin) and not a real? [duplicate]

I have been wondering why we say that a complex number is required to describe a property (state, amplitude) of a qubit. The property is a complex number with length 1, and for every probability there ...
2
votes
1answer
40 views

Behaviour of quantum spins

I am reading the Jordan-Wigner transformation in the book "Introduction to many-body physics" by Piers Coleman. When I read the introduction of this chapter, it is stated that: Quantum spins are ...
0
votes
1answer
69 views

Bell inequality proof

I am trying to understand how the correlation function in John Bell's paper on EPR is derived for a spin singlet state $|{\Psi}\rangle$. This is defined to be $$ \langle{\Psi}|\left(\bf{\sigma}\cdot\...
2
votes
2answers
63 views

Angular momentum coupling

I read about angular momentum coupling on wikipedia and there are a few things i dont understand. What does this mean "spin and orbital angular momentum of a single object belong to different Hilbert ...
0
votes
1answer
34 views

Does pseudospin necessarily carry angular momentum?

And if so, why? I was told that anything that mathematically transforms like a spin must carry angular momentum. Is this true? One example of pseudospin is electrons in graphene on the A and B ...
1
vote
0answers
55 views

When will Hund's rules fail?

I heard someone mentioned that Hund's rules do not always work. Looking at atomic spectrum: (https://qudev.phys.ethz.ch/phys4/PHYS4_lecture10v1_2page.pdf page 10 Hg spectrum) How could singlet (with ...
1
vote
1answer
62 views

Why are Pauli vectors for different particles opposite in the singlet state?

If $\boldsymbol{\sigma_{1}}$ is the Pauli vector for a particle and $\boldsymbol{\sigma_{2}}$ for the other particle, why is $\boldsymbol{\sigma_{1}}=-\boldsymbol{\sigma_{2}}$ in the singlet state? I ...
0
votes
1answer
31 views

Decay of spin-1 particle into two spin-0 particles

If we consider the decay of a spin-1 particle with spin projection $m_s=1$ into two (distinguishable) spin-0 particles, what are the possible values of the orbital angular momenta $l$ of the resultant ...
0
votes
1answer
93 views

What are “the correct spin operators” mentioned in the book “Quantum Field Theory” by Lewis H. Ryder?

In subchapter $2.7$ ("The relevance of the Poincaré group", page 63), to be found in this link, Ryder writes: The correct spin operators are rather complicated in form and the interested reader is ...
2
votes
0answers
28 views

Why can the spin operator be written as a product of fermions?

I was studying the Hubbard model, where we define the spin operator $\vec{S} = \frac{1}{2} c^\dagger \vec{\sigma} c$, where the creation and annihilation operators are both vectors of the form $c^\...
1
vote
1answer
62 views

Representing a reducible Cartesian tensor as a spherical tensor

I'm quite confused by this transformation, and am trying to gain fluency in moving back and forth between these objects. I understand that a second order dyadic Cartesian tensor can be represented as ...
0
votes
0answers
13 views

Measuring the lorentz transform generators $J$, $K$, and providing evidence that photons have no internal continuous d.o.f

I am reading Weinberg's first QFT book. We looked for (and I suppose found) unitary representations of the Lorentz group: $$U(\Lambda) = 1 - i (\vec{\theta}\cdot\vec{J}-\vec{\eta}\cdot \vec{K})$$ ...
2
votes
1answer
19 views

Radial term in the spin-orbit coupling

The spin-orbit interaction for the hydrogen atom is of the form $\hat{H_1} = A\frac{1}{r^3}\pmb{\hat{L}}\cdot \pmb{\hat{S}}$ Now in my course, we treated this interaction by working in the basis of ...
3
votes
1answer
134 views

Nature of Spin in QFT

If the orbital angular momentum of an electron in an atomic orbital is associated with (generated by) an asymmetry in the orbital wave function, is it also the case that the intrinsic spin of a free ...
-1
votes
1answer
64 views

Can we use the Pascal triangle as an aid to construct superpositions of wavefunctions corresponding to $n$ electron spins?

Suppose we have n electrons and want to construct the wavefunction corresponding to the spins of the electrons. Can we construct this wavefunction (in the $(s_1,s_2,s_3 ... s_n)$ representation, so ...
2
votes
1answer
83 views

Infinite vs Finite dimensional Hilbert space

Let us consider an electron in an infinite square well. As we know that the electron has a spin=$1/2$ . The spin operator ($z$-direction) has two eigenvectors which span the vector space. But if we ...
3
votes
1answer
53 views

If both the eigenvector of $S_z$ and $\hat x$ form a basis for our Hilbert space, how can it have different dimensions?

In almost all the books on Quantum Mechanics, it is stated that if $|\alpha \rangle $ is a ket describing the state of a system, then any observable has a set of eigenvectors s.t those ...
2
votes
3answers
89 views

What happens to the spin when photon is absorbed by an electron?

Photon is spin 1 and electron is spin 1/2, so when a photon is absorbed by an electron it is destroyed and the electron becomes excited by that amount of energy. The next moment the electron will go ...
1
vote
1answer
35 views

Problem on measurement of spin of an electron

I came across a problem which reads: "An electron is initially found to have z-component of spin=+h/4π. Then a measurement of component of its spin along x-direction is carried out but the result is ...
3
votes
2answers
138 views

Why does the triplet state $\dfrac{1}{\sqrt{2}}(\uparrow\downarrow+\downarrow\uparrow)$ have spin 1 and not 0?

Don't the spins in the state $\dfrac{1}{\sqrt{2}}(\uparrow\downarrow+\downarrow\uparrow)$ cancel each other so that the total spin is 0 just like for the singlet state $\dfrac{1}{\sqrt{2}}(\uparrow\...
2
votes
1answer
71 views

What is difference between fermions and spins?

A spin model i.e. $H_s = \sum_i^{L-1} S_i^x\cdot S_{i+1}^x$ can be written in matrix form as following $$H_s = \big(S_1^x \otimes S_2^x \otimes I_3^2 \otimes I_4^2\otimes \cdots\otimes I_{L-1}^2\big)...
0
votes
1answer
24 views

Question about the perturbation solution involved Rashba spin-orbit coupling?

Currently, I am reading the original paper about spin field effect transistor proposed by Supriyo Datta and Biswajit Das. In the last part of this paper, to obtain a larger overall current modulation ...
0
votes
2answers
48 views

Entanglement, measurements and correlation

I am studying for my quantum mechanics exam and I came across the following question, I hope I reason correctly. Consider two spin-$\frac{1}{2}$ systems one of which is measured by Alice and one ...
4
votes
0answers
40 views

How does one electron or spin see the other in a ferromagnetic material?

QM tells us that only one component of angular momentum is measurable which conventionally taken to be Lz= 1/2. The other two components have an uncertain magnitude and direction and this is usually ...
0
votes
1answer
74 views

Spin (helicity) and polarizations of photons: are they secretly related?

Edit Circularly polarized photons have $$\textbf{S}\cdot\hat{\textbf{p}}=\pm \hbar\tag{1}$$ and it also satisfies $$\boldsymbol{\epsilon}\cdot\hat{\textbf{p}}=0\tag{2}$$ where $\textbf{S}$ is the spin,...
0
votes
2answers
31 views

Entangled photons production and interference

Can entangled photons be produced simultaneously and have the same frequency and opposite polarization spins? What can happen if this pair is led to interfere with each other? If they are cancelling ...
0
votes
2answers
48 views

Are all Bell tests valid only for linearly-polarized photons? [duplicate]

In https://arxiv.org/abs/1407.2605, it is argued that all photons are necessarily circularly polarized, and linearly-polarized photons must be a superposition of such circularly-polarized photons. ...
0
votes
1answer
48 views

Total angular momentum of three spin-1/2 particle state calculation

I've come across a problem involving a system with three spin-1/2 particles in a given state, for which the total (spin) angular momentum can be calculated using the $\hat{S}^2$ operator in the ...
15
votes
1answer
267 views

What is the spin-statistics theorem in higher dimensions?

In $d = 3+1$ dimensions, the spin-statistics theorem states that fermionic particles have half-integer spin and bosonic particles have integer spin, in a well-behaved relativistic quantum field theory....
0
votes
2answers
31 views

Doing Stern-Gerlach experiment without blocking the atoms in the $-x$ direction

In quantum mechanics, in general, it is stated that the act of measurement changes the state of the system. For example, consider the following Stern-Gerlach setup; A beam of silver atoms first ...
0
votes
3answers
112 views

Why are Spin 1/2 particles invariant to $4\pi$ rotation loops while Spin 1 particles are invariant to $2\pi$ loops?

Why do Spin 1/2 particles when turning them by 360 deg get a phase factor of -1 and a loop of 720 deg leads to the identity while for spin 1 particles a loop of 360 deg gives already the identity?
0
votes
2answers
48 views

Why do we consider spin degeneracy in graphene quantum hall effect and not in the conventional one?

When dealing with quantum hall effect in graphene we say that each landau level (with $n\neq 0$) has 4 times the degeneracy of a simple landau level derived for an electron in a magnetic field because ...
-1
votes
1answer
29 views

What is the term for a particle spin's uncollapsed position? What is the orbiting “thing”?

I'm not sure if I have the correct visual model, but I imagine that a particle spin can be represented by a single point on the orbit, or by a superposition state (like a random plane through a corner ...