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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104 views

Bell's theorem: why does correlation = cosine rule out hidden variables?

I was reading about entanglement and bell's theorem and played around with the idea. Specifically the point that the correlation of the measurement of entangled electrons at arbitrary angles is given ...
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Can we identify configurations of the classical Heisenberg model with pure states of the spin-${1\over2}$ quantum Heisenberg model?

My background is mostly probability theory with some elementary quantum mechanics. Consider the following (very informal) "dictionary" between classical and quantum models for a particle in ...
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Putting a boson or any other particle in a 3D potential well

I am confused as to how putting a different particle with a different spin change the equation of the particle in a 3D potential well (all of same side length). For a particle in a box, the wave ...
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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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Describing a subspace of a Hilbert space of $N$ spins 1/2

Consider having $N$ spins $1/2$, so the overall state of $N$ particles can be described by the total spin value $S=0 \ldots N/2$ (let us set $N$ to be even for simplicity), and the projection of the ...
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Ramsey technique and spin echos

Assuming we use a laser of frequency very close to resonance, in the Ramsey technique (say for 2 level atoms) the $\pi/2$ pulse would put the Bloch vector in the equatorial plane, along the y axis, ...
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113 views

Why are these open string oscillation modes identified with spin 1 particles on the brane?

On page 55 of David Tong's String Theory lecture notes, during the discussion of the first excited states of open strings, two classes of states are identified, both of which are massless. The first ...
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Aren't measurements in the Stern Gerlach experiment inherently intrusive to the states of particles?

The Stern Gerlach experiment that established the quantization of spin in a particular direction, according to my understanding, does so while inevitably affecting the particle. To conduct a ...
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Why does the Dirac beta matrix commute with the angular momentum operator?

This is the Dirac Hamiltonian, and Beta is The question says it all, I don't understand why Beta would commute with $ \hat L$
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Stern-Gerlach experiment with a magnetic field inbetween

An experiment is set up so that a beam of spin-1/2 is prepared for $S_{z} = \hbar/2$, it then passes a constant magnetic field $\textbf{B} = B_{0}\textbf{e}_{x}$ with the velcity $v_{0}$ for a ...
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How does parity act on relativistic one-particle states?

Please allow me to set the context based on my understanding before I present the question. In quantum field theory, one-particle states are the basis states of the infinite-dimensional unitary ...
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Why we don't observe a magnetic field on the nucleus due to electron orbit?

When we study the spin-orbit interaction, we only find the electric field in the frame of the nucleus, while in the electron referential frame, we find the magnetic field due to the relative orbit of ...
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Wavefunctions as Inner Product

In the following expression, n and m belong to the number basis and x is the position: $$ \langle n|m \rangle = \int_x n^*(x) m(x) dx = \int_x \langle n|x \rangle \langle x|m \rangle dx $$ I ...
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How many degrees of freedom of $n$ spin 1/2 particles (discard spatial degrees of freedom)?

I think the state of the system can be expanded by basis $\{|000...0\rangle,|100...0\rangle,...|111...1\rangle\}$. So we can be completely certain of this state if we know the coefficient of these $2^{...
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How do I experimentally figure out what the statistical operator $ρ$ is?

A general statistical operator can be expressed as a 2x2 matrix in the form of $$\left(\begin{array}{cc}p& r-ic\\ r+ic& 1-p\end{array}\right)$$ where p is probability and r and c are real ...
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Combining spins of two particles of spin |1,0> and |1/2, 1/2>

I am trying to combine the spin of two particles. Their individual spins are: $|1,0\rangle $ and $\left|\frac{1}{2},\frac{1}{2} \right>$ Now I am told that they combine to give a total spin state ...
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Bounding the value of a function for separable spin states

Consider $N$ spin-1/2, for which we can define the collective spin operator $\vec{S}=\sum_i \frac{\vec{\sigma}^{(i)}}{2}$. My question is, what is the upper bound $U$ on $$ f(\rho) = \text{Var}[ S_z ] ...
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Questions regarding particle spin

I have two queries regarding the spin of particles. Can we talk on the conservation of spin? Citing this, the answerer writes that spin is intrinsic angular momentum, but what exactly do you mean by ...
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Entangled spin anti-correlations observed relative to what?

Alice and Bob work in a large room. In the middle of the room, they have a device that generates spin-entangled particle pairs; one member of each pair goes to Alice’s bench, the other one, to Bob’s. ...
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Why don't elementary particles with spin $\frac{3}{2}$ exist? [duplicate]

The question is simple: why aren't there elementary particles to be found in Nature which have an intrinsic spin of $\frac{3}{2}$? Do the laws of physics (say, quantum field theory) prohibit their ...
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Spin 1 particle through two Stern Gerlach apparatuses, one oriented along the z-axis, the other is at an angle

In class, we solved this problem: There is a Stern Gerlach apparatus oriented along the z-axis. A spin 1 particle goes through this, the states are called $|u_+\rangle$, $|u_0\rangle$ and $|u_-\rangle$...
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Confused how to solve my equation of operators

I am trying to show $[J_x,J_y] = i\hbar J_z$ commutation relation for the operators. I have so far expanded to get: $$=(L_xL_y+L_xS_y+S_xL_y+S_xS_y)-(L_yL_x+L_yS_x+S_yL_x+S_yS_x)$$ Giving: $$ = [L_x,...
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Can the magnetic moments of particles rotate due to non-uniform magnetic field in the Stern-Gerlach experiment?

Does this play any role in the splitting of particles or is this effect very little to be even considered? I am not sure, but I feel like that for a non-aligned magnetic moment, the nonuniform ...
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Different ways to orient the spin in the same direction

I know that all electrons have quantised spin. But how can one orient all the spins of a given bunch of an electrons in the same direction? I know one way is that we pass the electrons through a ...
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Why do photons have spin of 1 when they have no mass? [duplicate]

How can a photon have a spin of $1$ when it has no mass? Since the spin is intrinsic angular momentum, if $m = 0$, then the spin must be zero.
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How many parameters are needed to specify a quantum state?

We have a spin state \begin{align} \ |{\Psi}\rangle=a_u|{U}\rangle+a_d|{D}\rangle \end{align} where $|U\rangle$ and $|D\rangle$ are $up$ and $down$ basis vectors, and $a_u$,$a_d$ are their complex ...
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Magnetic field perceived by the electron

This section presents a relatively simple and quantitative description of the spin-orbit interaction for an electron bound to a hydrogen-like atom, up to first order in perturbation theory, using some ...
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Defining particles by their commutation/anti-commutation relations

In my studies of many-body physics, I have encountered three types of particles, which can be defined based on their commutation/anti-commutation relations. Fermions, defined by raising/lowering ...
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Is there a Relationship between thermal Hall conductivity and coplanar/non-coplanar spin?

Does the magnitude of the thermal Hall conductivity depend on whether spins are coplanar or not? Also, if you have any theoretical references, it would be helpful if you could present them.
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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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Finding the direction of a Spin-State

Given a non normalized state, find the direction of the state $\chi$?: $$ \chi = (1+i)\chi_{+}^{z}-(1+i\sqrt{3})\chi_{-}^{z}$$ Where $\chi_{+}^{z}, \chi_{-}^{z}$ are eigenstates of $S_{z}$. I know ...
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Geometric Interpretation of Rotated basis of Hamiltonian and collective Dicke states

Suppose I start with a basis of states for a two spin-1/2 particle system, namely, $\{\left|\uparrow\uparrow\right\rangle, \left|\downarrow\downarrow\right\rangle, \left|\uparrow\downarrow\right\...
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what are the possible values of the total spin S for a system of three electrons?

I thought given that electrons have spin $\pm \frac{1}{2}$, the values would be $\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$, $\frac{1}{2}+\frac{1}{2}-\frac{1}{2}$, $\frac{1}{2}-\frac{1}{2}-\frac{1}{2}$ and $...
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How to symmetrize the canonical stress-energy tensor? [duplicate]

Given the Lagrangian density for a real scalar field $\mathcal{L}(\phi, \partial_\mu \phi)$, we obtain from Noether's theorem the canonical stress-energy tensor $$ T^{\mu\nu} = \frac{\partial \mathcal{...
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Zee Quantum Field Theory page 35

About spin 2 polarization tensors $$\varepsilon_{\mu\nu}^{(a)}, $$ it is claimed that $$\sum_{a} \varepsilon_{\mu\nu}^{(a)}(k)\varepsilon_{\lambda\sigma}^{(a)}(k) = A(G_{\mu\lambda}G_{\nu\sigma}+G_{\...
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Constant expectation values for spin components of Dirac particles

My question is largely related to this one: Spin expectation values in Dirac theory It regards a free Dirac particle, with spin z+ in its rest frame, and moving with momentum in the x direction as ...
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Does Spin-Orbital Coupling (SOC) have no effects on orbitals with different $l$?

SOC term is: $$H_{\mathrm{SOC}}=\alpha \vec{L} \cdot \vec{S}=\frac{\alpha}{2}\left(L^{+} \sigma^{+}+L^{-} \sigma^{-}+L^{z} \sigma^{z}\right)$$ from spin Orbital Coupling matrix in p-orbital basis, we ...
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Why Is an Inhomogenous Magnetic Field Used in the Stern Gerlach Experiment?

The apparatus used in the Stern Gerlach experiment is somewhat like the one shown below with magnetic pole pieces of different shapes producing an inhomogeneous magnetic field. But what would have ...
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Is the expectation value of spin in magnetic field independent of time?

I am doing a homework problem on spin precession. Constant magnetic field $\vec{B}$ is in the z-direction. Initially, the electron is in an eigen state of $\vec{\sigma}.\vec{n}$, where $\vec{\sigma}$ ...
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Counting spin degeneracies

Let's say that given an ensemble of $N$ spin-1 particles, I want to find the number of degeneracies. For this example, let's just assume that only the spin of the particle gives us degeneracies. For ...
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Why is the spin of the graviton 2? [duplicate]

Electromagnetic and gravitational interactions are similar - they are mediated by massless particles, they have infinite range and they diminish with $1/r^2$. The main difference is that gravity is ...
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Total spin in a multiparticle system

I know that if I have a single fermion then the expectation value of the spin along the $\hat{n}$ direction can be computed by $\sigma \cdot \hat{n}$, where $\sigma_i$ are the pauli matrices. Now if ...
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How do the momentum and spin of negative energy electrons (particles in the Dirac sea) and positrons (holes in the Dirac sea) differ?

How do the momentum and spin of negative energy electrons (particles in the Dirac sea) and positrons (holes in the Dirac sea) differ? I just know that negative energy electrons and positrons have ...
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How do you align antiferromagnetic domains?

A natural property if ferromagnets, like iron, is that they form magnetic domains with moments pointing in random orientations. However, one can align all of these domains by applying an external ...
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Sidebands in spin-oscillator coupled devices

I am researching spin-oscillator hybrid devices (particularly those coupled to NV centers), and I have come across this paper investigating the strain field of a cantilever and its effect on the NV ...
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EOM, spin and mass of a particle described by a given Lagrangian

Consider the Lagrangian density $$L=\frac{1}{12}A^{\alpha \beta \gamma}A_{\alpha \beta \gamma}$$ and $B_{\alpha \beta}$, an antisymmetric two-indices, 4 dimensional, free field; moreover $A_{\alpha \...
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Pauli-Lubanski square operator

The Pauli-Lubanski operator is given by: $$ W_\mu = -\frac{1}{2} \epsilon_{\mu \nu \rho \sigma} J^{\nu \rho}P^{\sigma}$$ Thus the square operator is given by: $$ W_\mu W^\mu = W^2 = -\frac{1}{4} \...
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Rotation operator from angular momentum or spin operator

My instructor on quantum physics just stated that the total angular momentum operator, $\hat{J}$, can be expressed as $\hat{J}=\hat{L}+\hat{S}$, where $\hat{L}$ is angular momentum operator ...
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What is actually spinning in quantum spin? [duplicate]

Some texts say quantum spin is analogous to the spin of a planet in that it gives a particle angular momentum and a magnetic moment. However, as subatomic particles are tiny, the surfaces of charged ...
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If we put a spin-1 particle inside the 3D potential well, What will be the density of states for the system?

What will the density of states be if the particle inside the 3d potential well is a spin 1 particle? $$\psi(x,y,z)_{n_x,n_y,n_z}= \left(\frac{2}{L}\right)^{3/2} \sin\left(\frac{n_x\pi x}{L}\right)\...

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