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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Finding Clebsch-Gordan Coefficients with Ladder Operators [closed]

The question asks to find the Clebsch-Gordan Coefficients of $$\Big\vert \frac{3}{2} \frac{1}{2} \Big\rangle = C_{0, \frac{1}{2}} \Big\vert 1 0 \Big\rangle \Big\vert \frac{1}{2} \frac{1}{2} \Big\...
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Spin-$\frac{1}{2}$ particles in chemistry

Electrons and protons are spin-$\frac{1}{2}$ particles, so under a rotation by 360$^\circ$, their wavefunction changes by a sign. They are also commonly found alone in chemical reactions, especially ...
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Introducing Spin operator in QM

What was the experimental facts used in the construction of spins in Quantum Mechanics? What forced W.pauli to invent the idea of spins ? Can there be other internal degrees of freedom yet to be ...
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Can I feed enough spin up electrons to a black hole to affect its angular momentum?

I was reading classical spin vs quantum field spin. I know spin in quantum mechanics is just a quantum number. But what happens if I try to intentionally feed many electrons all in the same spin state ...
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Hyperfine lifetime calculation: what is the spin eigenfunctions?

I'm trying to calculate the lifetime of the 21 cm line in hydrogen and have the following expression: $$\frac{1}{\tau} = \frac{4\alpha}{3}\omega_{if}^3|\langle a_f|\vec{x}|a_i\rangle|^2.$$ The ...
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About the rigour of replacing spins by hardcore Bosons

In literature one sometimes find that spins are replaced by hardcore bosons. Formally one replaces spin operators $\sigma^- \leftrightarrow a$, $\sigma^+ \leftrightarrow a^\dagger$, $\sigma_z \...
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Symmetry of the spin function and T0 and S states

$|T_0\rangle = \frac{1}{\sqrt{2}}(|\uparrow \downarrow\rangle + | \downarrow\uparrow\rangle )$ is a triplet state, whose spin function has to be symmetric. $|S \rangle = \frac{1}{\sqrt{2}}(|\...
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Why, precisely, do three elements in a row (iron, cobalt, nickel) show ferromagnetism, but not the elements below them on the table?

The same is true for Neodymium, Promethium and Samarium, right? But like the first three, they are consecutive, not above and below each other. Somehow only elements in those two ferromagnetic 'hot-...
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Is there any relation between spin and gravity? [closed]

Is there any relation between quantum spin and gravity? Are there experiments that show or motivate that there is or isn't a relation between the two?
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Quantum Numbers/state multiplicity - specifically concerned with the differences between $L$, $l$ and $S$, $s$

To put this into context, I will write out exactly what was on the lecture slide that confused me (I've also attached a picture, but I appreciate that text is preferred on here for search engine ...
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Precession and alignment in a magnetic field

I am very confused about the concept of alignment in a magnetic field. Perhaps I am also confusing two different phenomena and that may be the issue. My classical understanding of a dipole says that ...
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Can we change the spin of electron by applying electric field from ↑ to ↓ configuration?

I read in this forum a similary question with magnetic field. But is it possibile change the alignment of the spin with a electric field (DC or pulsant current) in a layer of metal? Probably the ...
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Second quantization notation - Hamiltonian on triplet state

So I'm struggling quite a bit with dirac notation and second quantization and it seems like no one wants to really do calculations step-by-step to at least get the notation right. We were given the ...
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Connection between the 'spin' and 'polarization' of relativistic and non-relativistic particles

Context 1 The spin $s$ of a relativistic particle of mass $m$ can be read off from the eigenvalue $s(s+1)$ of the operator $- \frac{W_\mu W^\mu}{m^2}$ in the rest frame of the particle where $W^\mu=\...
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An electron has no known internal structure, does that imply it has an unknown one?

I'm currently reading Alonso and Finn's Electromagnetism book. It explains that the spin contributes to the magnetic moment and is somewhat comparable to a rotation of the particle around its own ...
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effect of Jahn-Tellar distortion in energy bands

Is orbital degeneracy same as electronic degeneracy? When we mean bands are degenerate, is it like the bands are doubled or single? After Jahn-Tellar distortion what will happen to the energy bands?
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Difference between angular momentum $L$ and $J$ in quantum mechanics

what is the difference between angular momentum L and generalized angular momentum J and their components?
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Numerical method to find the roots of the expected value of a spin 2j state

Currently I am working with finding the solutions for the following problem: I have a unit sphere in which I have n points defined by their polar and azimuthal angles: $\theta_n , \phi_n$. I then do ...
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Expand Helmholtz energy to fourth order in m (magnetisation)

The energy of a system of spins is given by: $$H=\frac{1}2\sum_{i,j=1}(J\sigma_i\sigma_j-h\sum\sigma_i)$$ I found that we can rewrite in terms of magnetisation, $m=\sum\sigma_i/N$: $$E=-N(\frac{Jm^2}...
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How did Goudsmit and Uhlenbeck figure out the electron has spin $\frac{\hbar}{2}$?

Most stuff I read online says that to explain the Anomalous Zeeman Effect they had to assume the electron's gyromagnetic ratio is $\frac{-e}{m}$ instead of the classical $\frac{-e}{2m}$. But, since ...
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How to obtain a vector relation for the Rabi frequency?

In this paper by Golovach et al.: http://journals.aps.org/prb/abstract/10.1103/PhysRevB.74.165319 there is the following equation for spin evolution: $$\langle \dot{\bf{S}} \rangle=({\boldsymbol \...
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Can we define Spin-Chern number for original QAHE Haldane model?

In Haldane's original paper [5], he discusses the quantum anomalous Hall effect as being characterized by the so-called Chern number that is the surface integral of Berry curvature over the entire ...
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Intuitive “story” explaining how orientation of spin axis affects up/down observation?

Is there a "convenient fiction" that explains why the angle of an electron's spin axis affects the probability of it being observed in a spin up or spin down state? By "convenient fiction", I mean a ...
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Is there a weak hypercharge : spin-3/2 analogy?

So I was not trained as a particle physicist, but I left a table of particles on a post on Hacker News based on what little I do understand about the conservation of weak hypercharge and weak isospin. ...
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How do you rotate spin of an electron?

I can't seem to connect these two stories. Can you please help? I have heard that you have to turn electron by 720 degrees in order to get the same spin state. Has this been seen experimentally? How ...
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Why does the renormalizable theory have only those particles with helicity less than or equal to 1?

Let the helicity operator be $\frac{P \cdot J}{P^0}$ with an eigenvalue $\lambda$. Then why do renormalizable theories have $|\lambda| \le 1?$ (in general dimensions or in 4ds?) Also, what is the ...
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Doubts about the use of tensor product In quantum mechanics

I'm studying quantum mechanic in particular tensor product and Hilbert space (for the first time). I have some doubts and I would like to check if I have understood correctly. Factorization The ...
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Deriving the Pauli-Schrödinger equation from the Dirac equation

Since the Schrödinger Pauli equation describes a non-relativistic spin ½ particle. This equation must be an approximation of the Dirac equation in an electromagnetic field. I was trying to derive this ...
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When is separating the total wavefunction into a space part and a spin part possible?

The total wavefunction of an electron $\psi(\vec{r},s)$ can always be written as $$\psi(\vec{r},s)=\phi(\vec{r})\zeta_{s,m_s}$$ where $\phi(\vec{r})$ is the space part and $\zeta_{s,m_s}$ is the spin ...
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Spin of two identical particles

I read that when I have two identical particles with spin 1/2 there are 4 possibilities: |↓↓⟩,|↑↑⟩,|↑↓⟩,|↓↑⟩. Then since there is the symmetrization requirement I can take as eigenvalues the ...
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Matrix representation of spin-2 system? [closed]

I am surprised no one has asked this before, but what is the matrix representation of a spin-2 system? Also, what are the equivalent of the Pauli matrices for the system?
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Spin during gravitational collapse

During or upon the ending of the gravitational collapse of a rotating star, can it be reasonably hypothesized that a collision between particles of half-integral spin might result either in a change ...
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Spin states in hilbert space

Do spin states (for ex: $\langle u| $ & $\langle d| $ and $\langle l| $ & $\langle r| $) along different axes (x-, y-, z- axis) of a quantum object belong to the same Hilbert space (where $\...
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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 ...
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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 ...
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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 $\ell = 0$ ...
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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{...
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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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How is the isospin quantum number calculated?

$$\Lambda^+_c$$ and $$\Sigma_c^+$$ are both made up of the same quarks, and have the same I_3, but have different isospin quantum numbers. How is the isospin quantum number determined? Also is the ...
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Why do electrons in singly occupied states have parallel spin?

I've been reading about Hund's rule and I realized that the Pauli exclusion principle only says that the electrons singly occupy states first, and nothing about their spins needing to be parallel. Why ...
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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?
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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 ...
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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 $\hat{f}$...
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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}...
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Two spin-1 system and the projector onto total spin 2 subspace [closed]

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=...
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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 ...
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Interchange symmetry for states with identical particles

I was reading this web page about interchange symmetry for states with identical particles here: http://quantummechanics.ucsd.edu/ph130a/130_notes/node317.html The article states that the highest ...
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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 ...
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Klein-Gordon-Equation contains no Spin

I have a question about an argument used in Schwabl's "Advanced Quantum Mechanics" concerning the properties of the Klein-Gordan-Equation (see page 120): Since the eigenenergies of free solutions are ...
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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 ...