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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64 views

What is the systematic way to determine the spin of lowest-lying states of baryons like $uuu$, $ssd$, $uds$ etc?

I learned that for the lowest lying states, $uuu$, $sss$, $ddd$ can only have $J=\frac{3}{2}$ $uus$, $ddu$, $ddu$, $ssu$ etc can only have $J=\frac{1}{2},\frac{3}{2}$ $uds$ can have $J=\frac{1}{2}, \...
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Resources for spin-stabilized magnets

I will be carrying out an experiment investigating the factors that effect the speed of a spin stabilized magnet. Can someone provide resources or articles that talk about/ have formulas related to ...
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Spin 0 boson interaction

I have a question regarding the interaction of two spin 0 bosons in a shared harmonic oscillator. What would their first excited state be? I'm thinking that the total state has to be symmetric so ...
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Precise value of spin in Nms?

What is the exact value of the spin of a particle with a 'spin' of 'one'? In units of Nms (Newton-meter-second)? And does a boson really have a spin of exactly one, or has that been 'normalized'? ...
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Why should spin “degeneracy” of electron not be infinite?

When we calculate the density of states for an electron, in the standard way as done in statistical mechanics textbooks ( by integrating once over space, then integrating over $\theta$ and $\phi$ of ...
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59 views

In the ground state of helium what's the differing quantum number?

In the ground state of the helium atom, both the electrons have the same quantum numbers $(n,l,m)$ equal to $(1,0,0)$. By Pauli's exclusion principle, the fourth quantum number must be different. What ...
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Can the Pauli equation be used to derive the usual $\mathbf L\cdot \mathbf S$ spin-orbit coupling? If not, what's the simplest way?

Can the Pauli equation, $$ \left[{\frac {1}{2m}}({\boldsymbol {\sigma }}\cdot (\mathbf {p} -q\mathbf {A} ))^{2}+q\phi \right]|\psi \rangle =i\hbar {\frac {\partial }{\partial t}}|\psi \rangle, $$ be ...
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Fermion Superposition [closed]

In case of superposition of identical particles, we usually just add their amplitudes. For example, if we have several particles having the amplitudes of being in a particular quantum state $\psi_1, \...
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Reverse Clesbch Gordan coefficients

I'm quite unsatisfied with this answer, so I'm hoping to get an adequate one. I'm trying to understand how to compute the reverse CB coefficents. I'll provide the simplest example. If I have a $l =...
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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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187 views

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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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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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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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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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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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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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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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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Why do we use this diagram/model for elementary particles?

The model of elementary particles is analagous to the periodic table, which is organized not only beautifully, but also functionally. The typical model for the elementary particles that pops up ...
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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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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 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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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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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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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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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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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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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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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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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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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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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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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 ...
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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 ...
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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 ...
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Why do spinning electrons generate magnetic dipole moments?

Can the spin of electrons generate currents? If not, how does it create magnetic dipole moments?
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$j=\frac{1}{2}$ 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\...