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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2answers
82 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 ...
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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 ...
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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 ...
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72 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 ...
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60 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 ...
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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 ...
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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^\...
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89 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 ...
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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: $$U(\Lambda) = 1 - i (\vec{\theta}\cdot\vec{J}-\vec{\eta}\cdot \vec{K})$$ ...
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1answer
28 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 ...
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152 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 ...
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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 ...
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1answer
148 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 ...
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59 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 ...
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236 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 ...
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50 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 ...
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164 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\...
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92 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)...
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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 ...
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55 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 ...
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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 ...
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103 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,...
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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 ...
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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. ...
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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 ...
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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....
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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 ...
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262 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?
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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 ...
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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 ...
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What's the opposite of spin collapse? Superposition as a verb?

With regard to photon spin, I'm trying to figure out what the word is for being "more random" as opposed to collapsing and being "more determined" If I were to say "the spin collapsed", how would I ...
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Will entangeld particles stay entangled?

I want to consider an experiment: We create two entangled particles a and b such that the spin of each is opposite to the other. We then measure spin in z direction (1). So we get a is up and b is ...
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Must the total orbital angular momentum quantum number $L$ be less than the principal quantum number $n$? If so, why?

I am studying LS coupling and term symbols. In my textbook, there is an exercise: Why is it impossible for a $2\ ^{2}\text{D}_{3/2}$ state to exist? The answer says, the total orbital angular ...
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Conjugate of total spin operator

I got a lattice, and the total spin operator for x and for y, for that lattice. I know that the x component conmutes with an operator called staggered spin operator in y. I also know that the ...
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Spin-orbit interaction for titanium in the excited state $(3d)^1(4p)^1$

Let's look at a Ti-atom in an excited state with 2 valence electrons $(3d)^1(4p)^1$. What term schemes $^{2S+1}L_J$ do we have for this state considering spin-orbit interaction? My take: For both ...
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81 views

Bosonic representation of $SU(N)$: what values can $n_b$ take?

In Assa Auerbach's book on page 166, he describes the construction of a bosonic representation of $SU(N)$ where the generators $S^{mn} \rightarrow b^\dagger_m b_n$. I'm a bit confused about the ...
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How do you go about guessing the ground-state spin and parity of a nucleus?

How do you go about guessing the ground-state spin and parity of a nucleus? Questions of this form seem to be asked frequently here, e.g., for 19F, 23Na, and 87Rb and 40K.
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Computing the spin degrees of freedom for a massless particle in $D$ dimensions

According to the paper A Lagrangian formulation of the classical and quantum dynamics of spinning particles, a relativistic spinless particle in $D$ spacetime dimensions can be described by the ...
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172 views

Why does Fluorine-19 have a nuclear spin of 1/2?

According to the nuclear shell model, $^{19}F$ has one unpaired proton in the $6$-fold degenerate $1d_{5/2}$ state, which means the orbital angular momentum is $l = 2$ and the total angular momentum ...
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Zero field splitting only defined for $S>\frac{1}{2}$?

Why do we only consider the spin-spin interaction between unpaired electrons? For reference the wikipedia page for zero field splitting says The classic case for ZFS is the spin triplet, i.e., the ...
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How to experimentally measure spin of photon?

Given that we know the spin of photon should be +1 or - 1, is there any experiment to directly measure and confirm it? I looked up stern-gerlach experiment is used on charged particle not photon.
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Deriving spin rotation with the commutator of function relation

I'm trying to derive the rotation effect of the spin operator from the commutation relation (from here): $$\left[f(A), B\right] = \left[A, B \right]\frac{\partial f}{\partial A}$$ I started by doing: ...
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How is a NMR spectrum obtained?

I am reading about NMR, and from what I'm understanding it should give information on the transition energies in the spectrum of the nuclear spin in a magnetic field. What I don't understand is how ...
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370 views

Wave function of a system of two identical fermions

In N. Zettili's 'Quantum Mechanics Concepts and Applications' [chapter 8, solved problem 8.3], we have to find wave function and ground state energy of a system having two identical fermions and in ...
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Action of rotation operator on spin 1/2 system

In Sakurai book on QM in chapter 3, he states the following relation $$e^{\frac{iS_z\phi}{\hbar}}[(\rvert+\rangle\langle-\rvert)+(\rvert-\rangle\langle+\rvert)]e^{\frac{-iS_z\phi}{\hbar}}$$ $$=e^{\...
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Intuition for the supertrace identity in supersymmetry

In pretty much every introductory book/lecture notes I've come across, one finds the expression for the mass matrices for scalars, fermions and vector bosons for a generic Lagrangian, and simply ...
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1answer
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Conformal Ward identities for spinor operators

How do you derive conformal Ward identities for operators with spin? You can see in Penedones's notes (page 6) ( https://arxiv.org/abs/1608.04948 ) a brief derivation of Ward identities for general ...
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2answers
103 views

Commutation relations

Given that the Hamiltonian for Muonium spin in zero magnetic field is $$\hat{H} = a \vec I \cdot \vec J$$ where $\vec I$ is the spin of a muon, and $\vec J$ is the spin of the electron, what is the ...
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Spin conservation in spontaneous parametric down-conversion (SPDC)

If one pump photon "decays" through the process of spontaneous parametric down-conversion into two photons how can the spin be conserved?
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225 views

How can I explicitly express the Ising Hamiltonian in matrix form?

I am reading this book about numerical methods in physics. It has the following question: Consider the Ising Hamiltonian defined as following $$H=-\sum_ {i=1}^{N-1} \sigma_i^x \sigma_ {i+1} ^x + h ...