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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Coupling of two spin half particles

If there are two electrons coupled by interaction having hamiltonian H=A*S1*S2 where S1 and S2 are spin angular momentum operators of two electrons, we know we have four possible eigenstates for the ...
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Rotation of second quantized operator in Fock space

I'm quite familiar with rotation in quantum/classical mechanics. I know rotation for an operator $O$ or state $|\psi \rangle$ acts like: $$O \rightarrow R O R^{-1} \\ |\psi \rangle \rightarrow R |\...
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Stern-Gerlach experiment for spin-1 particles

If we have a beam of spin-1 particles and let them pass through a Stern-Gerlach apparatus (oriented along z-axis, we get three output beams. Suppose we now take only the $+\hbar$ beam and pass it ...
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How to calculate 3 steps in Stern–Gerlach experiment? [closed]

How can we calculate Output3 and Output4, see picture If we defined vectors: up(T,p)=[cos(T/2)(cos(-p/2)+isin(-p/2)); sin(T/2)(cos(p/2)+isin(p/2))] um(T,p)=[-sin(T/2)(cos(-p/2)+isin(-p/2));cos(T/2)...
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Can Pauli matrix ($\sigma_z$) represent spin?

Can Pauli matrix ($\sigma_z$) represent spin? For example, when the eigenvalue of $\sigma_z$ is 1, the spin is up. We know the spin operator $S_z=\hbar/2*\sigma_z$.
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Regarding spin Hall effect and Thomas precession

I was reading about Mathisson–Papapetrou–Dixon equations which describe the motion of massive spinning particles. I am wondering if these sets of equations are just a quantum version of the classical ...
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In quantum mechanics (QM), can we define a higher-dimensional “spin” angular momentum other than the ordinary 3D one?

Inspired by my previous question Questions about angular momentum and 3-dimensional(3D) space? and another relevant question How to define orbital angular momentum in other than three dimensions? , ...
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Adding 3 electron spins

I've learned how to add two 1/2-spins, which you can do with C-G-coefficients. There are 4 states (one singlet, three triplet states). States are symmetric or antisymmetric and the quantum numbers ...
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Spin connection, curvature

5D Ricci Curvature I have a question about the calculation about the answer of the above link. They define the vielbein $\omega^\psi = e^\sigma[d\psi+A]$ and differentiate it, $d\omega^\psi = e^\sigma\...
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Relationship between optical coherence and spin dephasing?

I'm curious if there's a relationship between the inhomogeneous spin dephasing and the optical coherence of a material. Certainly, in many applications quantum information applications, you want both ...
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Is the electron spin $g$-factor value implying the particle is a composite one?

As I understood the highest possible value for a magnetic moment of a point charge having the same amount of charge as an electron and rotating with same electron velocity and confined in the same ...
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In what circumstances, can exchange interaction acquire temperature dependence?

Heisenberg exchange interaction (sometimes called as magnetic stiffness?), originating from the Coulomb interaction and the Fermion statistics, is widely used in theories of magnetism. Conventionally, ...
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What are the 'good' quantum numbers for the weak- and strong-field Zeeman effect?

I'm quite confused on the 'good' quantum numbers. I thought the good quantum numbers could be defined as the quantum numbers which corresponding operators commute with each other and the Hamiltonian. ...
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spin direction of the electromagnetic field tensor

I guess the electromagnetic field strength tensor $F_{\mu\nu}$ can be considered as a spin-1 field. So, is it possible to derive $F_{\mu\nu}$'s spin direction based on the elements in the tensor (the $...
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Inversion symmetry on surface and spin

Let us assume you have a 3D bulk periodic crystal which has inversion symmetry e.g. $r\rightarrow -r$. Assume we are considering spinful operators with $S=1/2$. Now let us imagine cutting a surface ...
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Mirror symmetry of spin-1/2 wavefunction: Definition of the reflection operator

I would expect from a reflection operator $\hat{M}$ to leave a wavefunction unchanged if two times applied, thus $\hat{M}^2=1$. However, for a spin-1/2 particle this is not the case when following the ...
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Does the spatial part of the wavefunction need to be antisymmetric in the singlet and symmetric in the triplet?

Two spin-1/2 particles either are part of a spin-1 triplet or a spin-0 singlet. The singlet is antisymmetric but bosons need to be symmetric wave functions. So does the spatial part of the wave ...
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Spin-flip of electrons in non-neutral hydrogen atoms in water and fat molecules

What is the Spin-flip of electrons in non-neutral hydrogen atoms in water and fat molecules? I know there is known spin-flip RF of electrons in neutral hydrogen atoms (hydrogen line). Thanks, Cheers
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How to calculate spin correlation function via spin coherent state?

I am following the Section 8.3.1 of Auerbach. I want to calculate spin correlation function via spin coherent state, i.e. the equation (8.28): $$\begin{aligned}\left\langle\mathbf{S}_{m} \cdot \mathbf{...
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What is residual interaction physically?

In any nuclei, if it is even-even or odd-even we can determine ground state spin and parity just by single particle shell model. But if in a odd-odd nuclei, we consider residual interaction to ...
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Photon nonzero Spin (Helicity?)

I had a simple question - how many different values can a photon present for spin angular momentum, given that it's spin is 1? And although I immediately thought "3, since j = 2s + 1" (j being the ...
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The order of Pauli matrices

Is there any special reason why Pauli matrices are: $\sigma _1=\left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \\ \end{array} \right)$, $\sigma _2=\left( \begin{array}{cc} 0 & -i \\ i & 0 \...
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Macroscopic properties of individual spins in a material (magnet) - and their behavior under rotations

I am wondering (A) about the influence of individual spins on the behavior of a macroscopic object (B) and about the influence of rotating the macroscopic object on the internal spins To approach ...
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How to calculate the expectation value in spin coherent state?

In Shankar, QFT and Condensed Matter, p73, it says $$\langle S,S|\vec S|SS\rangle=\vec kS,\tag{6.3}$$ $$\langle\Omega|\vec S|\Omega\rangle=S(\vec i \sin\theta \cos\phi+\vec j \sin\theta \sin\phi+\...
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How does the spin of a particle vary if it is measured several times? [closed]

I have three questions about 3 successive measurements of the spin of an electron. In the first measurement the spin is always measured to be +1/2 on the z-axis. Measurement 2 and measurement 3 are ...
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Interacting helical edge state and scattering process

Imagine if you have a 2D topological insulator system where you can bring together the helical edge states from the opposite boundaries to interact (say, by a voltage gate or by a narrow constriction)....
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Klein-gordon, Dirac equation and the spin of the particles [closed]

This question might seem basic, but how does one conclude that the Klein-Gordon equation describes spin zero particles but Dirac equation describes spin half particles. Thanks. EDIT: Adding more ...
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When creating term symbols, how do you know if the angular momentum $L$ is antisymmetric of symmetric?

For example I'm trying to get the term symbol of $(1s)^{2}(2s)^{2}(2p)^2$ . In the answers they state the following: The combination of angular momenta $L_1 = L_2 = 1$ gives $L = 2$ (symmetric), ...
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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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How to find an orthogonal quantum state? [closed]

In the question I have L = 1 and s = 1/2. First I had to find the quantum state for the highest m = m$_l$ + m$_s$ value which I did. To find the quantum states for the next highest m value I used the ...
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Does rotations acts on spin?

Rotations are part of the symmetries of nature I heard that electrons carry a spin 1/2 Q: How do rotations acts on the spin of an electron? The state of my reflection: irreducible representations of ...
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Evaluating $\sigma^{\mu\nu}F_{\mu\nu}=i\alpha \cdot E+\Sigma\cdot B$ matrix, spin dependent term in quadratic Dirac equation

I derive the quadratic form of Dirac equation as follows $$\lbrace[i\not \partial-e\not A]^2-m^2\rbrace\psi=\lbrace\left( i\partial-e A\right)^2 + \frac{1}{2i} \sigma^{\mu\nu}F_{\mu \nu}-m^2\rbrace\...
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The stark effect of Hydrogen

I have read the stark effect of Hydrogen (calculating energy levels of the n=2 states of a Hydrogen atom placed in an external uniform electric field along the positive z-direction) from Quantum ...
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Question about an Exercise with Time-Dependent Hamiltonian

I've been recently been assigned this exercise: Consider two spin 1/2 particles which are coupled through a time dependent interaction: $$ H(t) = a(t) s_1 \cdot s_2 $$ where $a(t)$ is a ...
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Path integral for spin?

I'm searching for the path integral formulation for a spin particle and haven't found any precise description yet. Is there a systematic way to construct a non-relativistic path integral formulation ...
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Why can we approximate massive particles as massless or vice versa?

Our descriptions of massless and massive particles are very different. For example: Massless particles have only two polarizations, which we call helicities. Spin projection on axes different than ...
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Symmetrisation of (fermionic) two-particle system without vs. with spin in wave function

I'm using D. J. Griffiths's textbook Introduction to Quantum Mechanics (3rd ed.) for my introductory university course on the subject. In chapter 5 (starting at section 5.1.1), he discusses the ...
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Berry curvature for spin in a magnetic field

Does anybody know how to compute the Berry curvature for a spin with angular momentum $s$ (so it's not the usual derivation you find for spin-$\frac{1}{2}$ particles in most textbooks) in a magnetic ...
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Stern-Gerlach sequential experiments

Lets suppose we have spin 1/2 particle and some sort of Stern-Gerlach experiment setup (SG from now on). So one SGz setup means one that is oriented for spin projection in z direction, similarly for ...
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Anomalous Zeeman Effect

I was reading splitting of spectral lines in magnetic field and my book says In anomalous Zeeman Effect, Classically, the ratio of orbital angular moment to angular momentum $|\vec{L}|$ gives ...
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Electric dipole transitions with and without spin-orbit interaction

I have a question, using the following energy levels: I am under the impression here that the possible electric dipole transitions are $4s \to 4p, 4p \to 5s, 4p \to 3d$ and vice versa obeying the ...
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Why is $L$-$S$ Coupling Dominant in Lower Atomic Number like Carbon and Silicon and $J$-$J$ in higher like Germanium and Arsenic?

Furthermore, a) Why is the order of domination in $L$-$S$ coupling: Spin-Spin correlation Residual Interaction Spin-Orbit Interaction b) While the order in $J$-$J$ coupling is: Spin-orbit ...
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How to understand the difference of spin wave excitation for ferromagnetism (quadratic dispersion) and anti-ferromagnetism (linear dispersion)?

As we know, the dispersion of spin excitation (magnon/spin wave) for ferromagnetic(FM) system is quadratic as $k\rightarrow 0$, but is linear for anti-ferromagnetic(AFM) system as $k\rightarrow 0$. I ...
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What does spin 0 mean exactly?

I heard two definitions: Spin 0 means that the particle has spherical symmetry, without any preferred axis. The spin value tells after which angle of rotation the wave function returns to itself: $2\...
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Paper with sequential Stern-Gerlach experiments

Often sequential Stern-Gerlach experiments are taken to motivate basic quantum mechanics. But I can't find a paper where these are actually carried out experimentally. I have two questions: Who was ...
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How to prove identity $\langle \mathbf{S} \rangle^2 + \langle \mathbf{Q} \rangle^2 = 4/3$ for any spin-1 wavefunction?

Is there an easy way to prove that for an arbitrary wavefunction of spin-one $$\langle \mathbf{S} \rangle^2 + \langle \mathbf{Q} \rangle^2 = 4/3$$ where $\mathbf{S} = (S_x, S_y, S_z)$ for spin-1, ...
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Why is there this relationship between quaternions and Pauli matrices?

I've just started studying quantum mechanics, and I've come across this correlation between Pauli matrices ($\sigma_i$) and quaternions which I can't grasp: namely, that $i\sigma_1$, $i\sigma_2$ and $...
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The relation between spin and weak gravity conjecture [closed]

Is there a relation between spin and the weak gravity conjecture? How to connect the weak gravity conjecture and spin?
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Plane Wave Spinor solutions in 2+1 dimensions

I have read that if we use 2+1 dimensional space instead of the standard 3+1d space used in quantum mechanics, we can write the Dirac equation as $$i \hbar \frac{\partial}{\partial t} \psi(r, t)=\...
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Neutrino Helicity and Uncertainty

In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase Neutrino are left-handed. The spin is in the opposite direction of motion. ...

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