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Is there a link between electron spin and magnetism? can a magnetic field also be thought of as a 'spin' field. If the eletron spin is linked to the magnetic field then can magnetic repulsion be caused be the pauli exclusion principle?
How is quantum entanglement done in practice for different particles with different properties eg. spin, polarization, etc.? Why is entanglement useful for quantum circuits?
*I am curious about how they are actually entangled and used. I don't know how is entanglement applied in practice so I...
I am very interested in how Pauli found the Pauli matrices, so I read his original paper, but it didn't give me the perspective I wanted, so I went to Mehra and Rechenberg, but here's the thing, after reading Volumes 1, 2 and most of volume 3, I can't find any mention of Pauli matrices anywhere...
I just learned about the Stern-Gerlach experiment and have some questions:
1: clearly there's no objective "up" or "down"--the directions are measured relative to the magnetic field, correct? And well always find just 2 spots of equal and opposite distance on the detector, implying the magnetic...
I'm trying to fill a conceptual gap I have in the history of physics
In 1922 Stern and Gerlach make their experiment, proving that electrons have intrinsic angular momentum, however it takes a while for people to understand this. At first they think this is somehow caused by quantization of...
Today we know that if you make successive Stern-Gerlach measurements the beam of atoms will split according to this formula:
> cos^2 (theta/2)
And this is something people back then could have figured out, they could have done many measurements, plotted the values, and realized it followed...
Spin 1/2 particles are two states system in C^2 and so it is natural for the rotations to be described by SU(2), for three states systems like spin - 1 particle, Why do we still use SU(2) and not SU(3) to describe the rotations? Is it possible to derive them without resorting to the eigenvalue...
HUP for spins reads
$$\langle\sigma_z^2\rangle\langle\sigma_x^2\rangle \ge \frac{1}{4}|\langle\sigma_y\rangle|^2$$
Right after measuring ##\sigma_z##, we know it exactly, and so ##\langle\sigma_z^2\rangle=0##.
However, HUP then implies that ##\langle\sigma_y^2\rangle=\infty##
Even if we say...
here is my attempt to implement using python
import numpy as np
import matplotlib.pyplot as plt
def initialize_spins(L):
"""Initialize a random spin configuration with unit magnitudes."""
spins = np.random.normal(size=(L, L, L, 3))
magnitudes = np.linalg.norm(spins, axis=-1...
I have read, what I believe, misleading articles about generating entangled electron pairs. Some suggesting the electron is split. But this isn't possible because it's an elementary particle with charge/mass and Spin properties. So how do we achieve generating entangled electrons with opposite...
Hi.
Question as in the summary.
Spin has no obvious classical interpretation but it is often a conserved quantity and considered as some sort of angular momentum. What do you need to establish that spin is a conserved quantity? I'm finding references to situations where spin is not a...
Assume spin 1/2 particle
So the spin operator gives +/- hbar/2
eg. S |n+> = +/- hbar/2 |n+>
But S= s(s+1) hbar = sqrt(3)/2 hbar
So I'm off by a factor of sqrt(3).
I suspect I am missing something fundamental about my understanding of spin.
My apologies and thanks in advance.
Here is my workings out:
$$$$
If a particle's spin of magnitude ##\frac {\hbar}{2}## is prepared along direction ##\vec r_1## and subsequently its spin is measured along direction ##\vec r_2 ## at an angle ##\vec \theta ## to ##\vec r_1##, the probability of its being found "spin up" along is...
I truly am not sure. I assume it is that because everything has inertia, an a tendency to remain in a constant state of motion, when the clothes are quickly spun around they cannot remain in a constant state of motion (of either rest or constant velocity), but the water is "pushed"/spun out of...
Hello everybody, I consider two electrons that have enough kinetic energy to reach their respective classical electron radius. This would be:
2.0514016772310431402e-13 J
The corresponding speed is v = 287336682 m/s.
The electric field is
E = \frac{k_{e}}{R_e^2} = 1.8133774657059088443 ×...
I understand how a massive, electrically charged spinning ball would have both angular momentum and a magnetic dipole, and i can see how the
Stern–Gerlach experiment shows that the magnetic dipole of an electron is quantized.
What kind of experiment demonstrates
a connection between electron...
I did some research online and found that "When certain elementary particles move through a magnetic field, they are deflected in a manner that suggests they have the properties of little magnets." To explain this phenomenon, physicists invented the concept of spin. So far so good.
What I...
Hi,
I would like to know why a particle with spin=0 can't posses a magnetic dipole moment?
Using Wigner-Eckart theorem for ##\langle j,1,m,0|j,m \rangle## I get ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}##
It seems like the right hand side is the magnetic dipole...
Does the magnetic field caused by moving particles depend on the particle spin value?
Eg a stream of say protons spin 1/2 is creating a magnetic field. If the particles are (say) lithium nuclei spin 3/2 instead, does that create the same strength field ? (same conditions of course)
Hi,
Given a spin in the state ##|z + \rangle##, i.e., pointing up along the z-axis what are the probabilities of measuring ##\pm \hbar/2## along ##\hat{n}##?
My problem is that I'm not sure to understand the statement. It seems like I have to find the probabilities of measuring an eigenvalue...
I have some questions regarding the expected exchange particles for gravitation.
From my understanding the following was valid:
We can linearize the equations of GTR for weak fields
"Quantum mechanics" (Schrödinger, Dirac equations) are linear
Those linear equations allow eigenstates and...
1) The Hilbert space for each particle and the system are:
##H_1={\ket{\frac{1}{2} \frac{1}{2}}; \ket{\frac{1}{2} -\frac{1}{2}}}##
##H_2={\ket{1 1}; \ket{1 0}; \ket{1 -1}}##
##H=H_1 \otimes H_2##
2) I'm not sure what "considering the total Hamiltonian" means, but I think that the two CSCO...
By the statement of the question, a solution must take the form
##\begin{pmatrix} \Psi_1 \\ \Psi_2 \end{pmatrix}##
and the energy operator will be as per usual ##\hat{E} = i\hbar \frac{\partial}{\partial t}##. I am confused by the fact that
##S_y = \frac{\hbar}{2} \begin{pmatrix} 0 & -i \\ i & 0...
I read that quantum spin is the measure of the angular momentum of a quantum object. Suppose you have a rotating Thing 1. Quantum objects bounce off of it then collide with Thing 2. Will this transfer angular momentum from Thing 1 to 2, causing it to rotate?
Hi everyone,
I’ve been thinking about this for a while and have done a bit of research but can’t seem to get a straight answer.
Aside from collision with another object in space, is there anything that could cause the Earth’s rotation to dramatically slow down? If a sufficiently massive object...
Hello everyone,
I hope I'm asking in the correct section, if not please point me.
I read a list of gravitational wave detection. I focused on black hole - black hole events and I noticed the resulting black hole spin is very similar about a=0.7. I didn't find any explanation for this.
List of...
Suppose that we have a system including two single (and identical) orbitals as shown in the attached image. Then, consider the states that we have two different spins on the two orbitals. It seems that because of the left right symmetry of the system the special part of teh wave function can not...
Hi Pfs
Rovelli defines spin networks in this paper
https://arxiv.org/abs/1004.1780
for a trivalent node Vn = 0 (the volume)
nodes begin to "get" volume with the four valent case.
take a cube or a tetrahedron, each vertex is linkes to 3 nodes so they would have a null volume.
things are...
According to Chapter 8 of Griffiths' book Introduction to Electrodynamics, the magnetization force that acts on a magnetic dipole is
$$F_M=\nabla (m \cdot B)$$,
where ##m## is the magnetic moment and ##B## is the magnetic field.
For a paramagnetic or diamagnetic particle...
I know how to construct Sy for spin = 1 case from the raising and lowering operators.
I get
$$
S_y=\frac{i\hbar}{\sqrt{2}}\begin{pmatrix}
0 & -1 & 0 \\ 1 & 0 & -1 \\ 0 & 1 & 0 \\
\end{pmatrix}
$$
From what I have seen, the eigenspinor for $\hbar$ is found by solving
$$...
I'm just starting to get into QFT as some self study. I've watched some lectures and videos, read some notes, and am trying to piece some things together.
Take ##U(1)_{EM}: L = \bar{\psi}[i\gamma^{\mu}(\partial_{\mu} - ieA_{\mu}) - m]\psi - 1/4 F_{\mu\nu}F^{\mu\nu}##
This allegedly governs spin...
Pin Groups are the double cover of the Orthogonal Group and Spin Groups are the double cover of the Special Orthogonal Group. Both sets of the double cover are considered to be groups, but it seems that only one of the sets of the double cover actually contains the identity element, which means...
##Z = \sum_{-i}^{i} = e^{-E_n \beta}##
##Z = \sum_{0}^j e^{nh\beta} + \sum_{0}^j e^{-nh\beta}##
Those sums are 2 finites geometric series
##Z = \frac{1- e^{h\beta(i+1)}}{1-e^{h\beta}} + \frac{1-e^{-h\beta(i+1)}}{1-e^{-h\beta}}##
I don't think this is ring since from that I can't get 2 sinh...
Hello guys, i want to ask you a question about orbital and spin dipole, and how this is going to influence diamagnetic or paramagnetic substances. So my question is: we know in a atom there is orbital and spin motion by electrons so possibly two magnetic dipoles. Is it correct to say that in...
Hi Pfs
Spin networks are defined by the way their links and their nodes are equipped with SU(2) representations and intertwiners.
Could you give an example of two different spin networks with the same number of nodes, links between them, the same coloring of the links (and their orientations)...
https://physics.stackexchange.com/questions/418865/why-does-an-electron-have-spin
I’ve been trying to do research on this and haven’t gotten a clear answer. It sounds like they get it through particle interactions, but I may be misreading it. Is there an answer to this? And if there is, how...
When the expectation value of spin in the z direction for one particle is zero and I make measurements for an even number of particles in the same state, do I get exactly half to be spin up and half to be spin down along the z direction? More generally, what does spin expectation value for one...
Hi Pfs
i found a paper:
https://arxiv.org/abs/math-ph/0306059
in which the author gives a definition of spin networks
it is at the bottom of page 5
the words node or vertex does not appear.
what do you think of it?
Does the author think that all the information is in the hilbert spaces on which...
So this expression is apparently in Sz basis? How can you see that?
How would it look in Sy basis for example?
The solution is following. They are putting Sz as a basis, bur how do you know that Sz is the basis here?
Thanks
Not sure how to mark the level, I know what the math in the Einstein field equations represents (stress energy tensor, Riemann curvature etc), but have no facility in doing anything with that math.
so take 2 black holes, with say 100 solar masses. A is not spinning, B is spinning at...
There is a passage in this book where I don't follow the logic;
In this short quotation from 'Quantum Mechanics: The Theoretical Minimum' by Leonard Susskind and Art Friedman
\mathcal{A} represents the apparatus that is performing the measurement
the apparatus can be oriented (in principle) in...
Was curious at the upper limit for neutron stars,
found this article stating one was found at around 700 / s
https://www.newscientist.com/article/dn8576-fast-spinning-neutron-star-smashes-speed-limit/
did not see the size, the article is behind a paywall, but it would have taken a radius of...
I googled it, and almost every source I find says something like this:
"These stars were then gravitationally attracted to each other to create gigantic clusters of stars enshrouded in clouds of gas. Eventually these groupings of stars come together through the attraction of gravity and...
Quantum spin is orientable so it takes place in a space with an even number of dimensions. What is that space?
If the space had an odd number of dimensions, then spin in that space wouldn't be orientable. But quantum spin is orientable.
We could say that it is Minkowski space, but that space...
In the paper
C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573
about quantum dots, it is stated that the basis vectors in the space of quantum states for a single cell...