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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21 views

Complex rabi frequency

I am learning quantum optics. In the book written by Scully includes complex rabi frequency, when dealing with $\Delta$ level configuration, the Hamiltonian including laser-atom interacting concludes ...
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Which book (or article) has detailed calculation for Quantum Heisenberg Model for three or four spins?

A I need to write a program to calculate Quantum Heisenberg Model for any number of spins (with or without external magnetic field). Each spin is spin 1/2. I know how to do this calculation for two ...
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What is the value of the inner product $_x\langle+|-\rangle$?

I know that $\left|_x\langle+|-\rangle\right|^2 = 1/2$, so is it just as simple as taking the square root of $1/2$? Thanks.
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Why is it that the Callan-Gross relation predicts that quark has spin 1/2?

I'm studying deep inelastic scattering, and currently at the part where they say the Callan-Gross relation: $$F_1 (x) = \frac{1}{2x} F_x (x)$$ where $F_1$ and $F_2$ are the dimensionless structure ...
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Finding energy Eigenvalue from two spin Hamiltonian

Let's consider a system of two spins, named spin 1 and spin 2. Let's also consider, in a Hamiltonian, spin part has been defined as $\sigma_1 \cdot \sigma_2$. For example: $$H= E_0 + \sigma_1 \...
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138 views

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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25 views

Representation of spin-$1/2$ operators in terms of Majorana fermions

I am reading Quantum Field Theory in Condensed Matter Physics by A.M. Tsvelik. In Chapter 20, it is claimed that introducing three Majorana fermions $\gamma^\mu_i$ on each site $i$ of the lattice (...
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What differences would be observed in the Stern-Gerlach experiment when using neutral fluorine (Z=9) and neutral sodium (N=11)

I have been working through some past exam papers for my Quantum Mechanics module, and one of the questions is what would be different about observing the results of the Stern-Gerlach experiment when ...
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Hydrogen hyperfine structure from H2-molecule, interacting H-atoms or independent H-atoms?

On hyperphysics the hyperfine structure of hydrogen is compared to that of deuterium: According the Hyperfine structure on Wikipedia In atoms, hyperfine structure arises from the energy of the ...
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Interaction between electrons in which the magnetic dipole moments interact more strongly than their electric fields

Asking a question Has anyone tried to incorporate the electrons magnetic dipole moment into the atomic orbital theory?, I was curious whether anyone has attempted to relate the intrinsic property of ...
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Trying to understand spin in quantum mechanics

I'm trying to understand the concept of spin in Quantum Mechanics. I'm reading "Road to Reality" by Penrose, which despite not being a textbook, is reputed to give one a deep insight into physical ...
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Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
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How does angular momentum get quantized? [duplicate]

We know that the magnitude and direction of angular momentum is quantized in quantum mechanics. We can explain the quantization with the help of quantum numbers. But actually who is responsible for ...
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Electron to electron interaction

I am interested to know if it would be possible to calculate the magnetic attraction between two electrons at zero space between their magnetic poles against electrostatic repulsion between them in ...
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Confusion about Stern-Gerlach experiment

Why does the particle always have the same spin magnitude $\pm \frac{1}{2}\hbar$? In classical mechanics we can split a vector into components but in quantum mechanics due to uncertainty principle ...
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Does spin add energy to a quantum mechanical system?

If a particle (let's say an electron, a 1/2 spin particle) has spin component $S_z=\hbar/2$. Does the spin contribute to the total energy of the electron? For example, without considering the spin, ...
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Understanding quantum spin

I'm trying to get an idea of what spin in quantum mechanics means. I have the following questions regarding spin: The eigenvalues of the operator corresponding to the z component of spin is $\hat{S}_{...
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What is the (triplet) eigenstate for two electrons? [duplicate]

Let's assume I have a harmonic oscillator which is one dimensional. What is my plan is to work the the two electron's spin states and my requirement is that they have to be in the triplet sates. Lets ...
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225 views

Good Quantum numbers in $L$-$S$ coupling

I'm having a hard time understanding a few things about L-S and j-j coupling in 2 (or more) electron atoms. What I picked up from our lectures is the following: The Hamiltonian can be "broken up" ...
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Mathematical Rigorousness of Taking the Thermodynamical limit of a finite size quantum model

Suppose I have nearest Neighbour Quantum Ising model with a transverse field. $$\hat{H} = \sum_{i}S^{x}_iS^{x}_{i+1} + h\sum_i S^{z}_i$$ Through Jordan-Wigner and Bogoliubov transformation, one finds ...
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158 views

How to produce a given entangled state of two quantum bits?

I was watching Leonard Susskind's video series on quantum entanglement, where he looks at the spins of two electrons. In particular, there are entangled states of the form $$\alpha\left|\uparrow \...
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zero spin particles' spin states

We know that the full wave function of spin particles have two parts. One is the spin part and another is the spatial part. Let's assume I have given a wave function which is the spatial part: $$\...
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356 views

Linear light polarization and photon spin

The following is from Wikipedia: "Circularly polarized electromagnetic waves are composed of photons with only one type of spin, either right- or left-hand. Linearly polarized waves consist of equal ...
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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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Question about choosing the time reversal operator

According to the "QFT Nutshell" page 102-104 about Time reversal, the author said about applying the time reversal to the spin 1/2 system. Let $T=UK$, where $K$ complex conjugates everything to ...
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Quantum Monte Carlo Loop Algorithm for quantum spin: why is the freezing graph present in ferromagnetic Ising model?

I study the loop algorithm (Evertz et al). I cannot understand, why the freezing graph type where we have to flip all 4 spins together is not present for the quantum-XY model and the anti-/...
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Gravitons from linearized gravity

Linearizing gravity as follows: $$ g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu} $$ Up to this point, everything is a 4x4 matrice. How does one eventually recover a spin-2 particle which, according to https:/...
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Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf j_{\...
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What is the 4-spin vector of a photon?

The photon, being a vector boson has 2 spin states, $\pm 1$. In relativity, we can determine the four-spin vector $s^{\mu}$ of a particle (see e.g. Costa et al. 2017). What would $s^{\mu}$ be for a ...
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Stern-Gerlach experiment interpretation [on hold]

It seems to me there is a problem with the usual interpretation of the Stern-Gerlach experiment. Sending a magnetic dipole on a path through a magnetic field would, on classical assumptions, affect ...
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130 views

Trouble understanding Sakurai's calculation of $\exp\left(\frac{iS_Z\phi}{\hbar}\right) \;S_x \; \exp\left(\frac{-iS_Z\phi}{\hbar}\right)$

I'm having some trouble with a derivation in Sakurai's Modern Quantum Mechanics (specifically Derivation 1 on §3.2, p. 159), where he computes $$ \exp\left(\frac{iS_Z\phi}{\hbar}\right) \;S_x \; \exp\...
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Correct Visualization of a Spin Wave in a Ferromagnetic material

One way of describe a ferromagnetic material is the Heisenberg hamiltonian $ H = -\frac{J}{2} \sum_{<i,j>} $S$_i$S$_j$ where $J$ measures the interaction between spins (positive for ...
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Has anyone tried to incorporate the electrons magnetic dipole moment into the atomic orbital theory?

The Pauli exclusion principle is related to the electrons spin. The quantum numbers are complete only with the spin quantum number. I am curious whether anyone has attempted to relate the intrinsic ...
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What magnetic interaction makes spin not conserved?

If $[S_i,H]\neq0$ or $[S^2,H]\neq0$, we might say spin is not a good quantum number in the system. But is there any more practical or detailed criterion? Or certain families of magnetic interaction ...
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Gilbert original paper (1955) reference

I'm looking for the Gilbert's original paper where he derives the gyromagnetic Landau Lifshitz Gilbert (LLG) equation of motion from a variational principle. Most of the people cite: Gilbert, ...
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Spin vs orbital angular momenta in QFT

I couldn't find past answers that quite match what I wanted, so I will try to ask in slightly different manner. In QM, we have total angular momentum operator $\vec{J}$ (I dropped the hat for ...
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Tunneling elements in the Hubbard model

Consider the tunneling Hamiltonian in the Hubbard model for a 1D lattice of quantum dots. $$\begin{align}\hat{H}_t=t\displaystyle\sum_{i,j,\sigma}c_{i,\sigma}^{\dagger}c_{j\sigma}+c^{\dagger}_{j,\...
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Direct measurement of $\mathbf S^2$

For concreteness, consider two spin-1/2 particles with spin vectors $\mathbf S_i=(S_i^x,S_i^y, S_i^z)$. The total Hilbertspace is four-dimensional, and as a basis we can take the (simultaneous) ...
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Does electron affinity decrease with charging?

Lets consider two materials A having higher electron affinity than B while both are not too far off. If they are both insulators and A accumulate charges due to triboelectric effect. Than after a ...
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Why is there no state of total spin 0 for spin-1 and spin-2?

To my understanding, decomposing the tensor product of two particles with spins $s_1$ and $s_2$ works as follows: $$\mathcal{H_{s_1}}\otimes \mathcal{H_{s_2}}=\mathcal{H_{s_1+s_2}}\oplus\mathcal{H_{...
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Constructing singlet state in second quantization formalism

I am trying to understand the second quantization formalism. Let's say we have a system of fermions (e.g. electrons) with spin in an array of quantum dots. The creation and annihilation operators $c^{\...
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Is the magnetic dipole of the electron an intrinsic property?

The profound answer to the question How permanent magnets work? starts with Sub-atomic particles such as electrons, protons, and neutrons (and many others) have a fundamental quantity called a spin ...
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Photon carries spin angular momentum of $\hbar$

I know from numerous articles and also wiki (http://en.wikipedia.org/wiki/Spin_angular_momentum_of_light) that a photon carries spin angular momentum of $\hbar$. How to prove it mathematically? What ...
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Why does a spinning nucleon generate a magnetic field?

I am trying to understand how NMR works, but I am not sure why a spinning nucleon produces a magnetic field. Is this a consequence of the quark structure inside?
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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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Using entangled qubits to communicate [duplicate]

After reading up on quantum mechanics considering entangled qubits I was asking myself this simple question: If one qubit (A) positioned on earth is entangled with another qubit (B) which is - say - ...
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Are there compelling reasons not to organize the elementary particles by charge and spin? [closed]

I don't like the way the standard model is currently displayed (see second picture for reference). It does a poor job of abstracting the information into something understandable. As far as I ...
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Did the Feynman heuristic of “simple effects have simple causes” fail for spin statistics?

Someone here recently noted that "The spin-statistics thing isn't a problem, it is a theorem (a demonstrably valid proposition), and it shouldn't be addressed, it should be understood and celebrated." ...
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Factorizing spin part and space of many electron wave function of an atom's ground state

I am trying to write the ground state wave function of a 10 electron atom as a product of space part and anti-symmetric spin part. $$1s\uparrow,1s\downarrow$$ $$2s\uparrow, 2s\downarrow$$ $$2p_{x}\...
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Quantum Mechanical Treatment of the Spin Echo

I'm trying to find the expectation value of the spin in the $y$ direction after applying a $\pi/2$-$\pi/2$ sequence of pulses. In Slichter's Principles of Magnetic Resonance, he does a $\pi/2$-$\pi$ ...