Spin Definition and 1000 Threads

Now then, if I intend to make a matrix pretaining to single transitions of the composite system, i align the states with fixed r. For fixed r I have 2m+1 states. When r=N/2 my states are N+1 as simple substitution verifies. However, when r=N/2 -1 the number of states are (N-1)^2. It gets weirder...

If a spin 1/2 particle we're to be rotating as it was passing through a Stern Gerlach experiment wouldn't this create particle paths which may switch from spin up to spin down or vice versa, or even oscillate in mid flight? If the experiment were done with a rapidly rotating silver atom source...

Background: For electric dipole radiation, the energy and angular momentum lost by radiation from a system of charges by radiation is given by: $$\dot{E}_{dip} = -\frac{2}{3c^3} \ddot{\textbf{d}}^2$$ $$\overline{ \dot{\textbf{M}}_{dip} } = -\frac{2}{3c^3}\overline{\dot{\textbf{d}} \times...

Given the full Lorentz group is ##O(3,1)## and the restricted Lorentz group is ##SO(3,1)##, the full Poincare group is ##\mathbb{R}^{3,1} \rtimes O(3,1)## and the restricted Poincare group is ##\mathbb{R}^{3,1} \rtimes SO(3,1)##. Given that ##O(3,1) = \mathbb{Z}_2 \rtimes SO(3,1)##, how might...

It is common lore that bosonic fields of odd spin, such as electromagnetism, cause equal charges to repel, while bosonic fields of even spin, as pions or gravitons, cause equal charges to attract. Has anyone seen this argument in a textbook? And its proof? Or is it just internet lore, or...

In the following expansion how to find the coefficients ##\alpha## and ##\beta##? $$|S, S_z\rangle = \alpha |S+1/2, S_z+1/2\rangle \otimes |1/2,-1/2\rangle + \beta |S+1/2, S_z-1/2\rangle \otimes |1/2,+1/2\rangle$$

TL;DR Summary: Find the possible outcomes of ]##L^2## and ##L_{z}## and their respective probabilities of an electron of an idrogen athom with function: ##\psi(r) = ze^{-\alpha r}## Hi guys, I have a problem with this exercise. The electron of a hydrogen atom is found with direct spin along...

If you have a magnetic monopole with non-zero spin, would this result in an electric dipole? Just like an electric charge with spin results in a magnetic dipole?

Since ##U## is a space and spin rotation, it would be $$U(R) = e^{-i\textbf{L}\cdot \hat{\textbf{n}}\phi/\hbar}\cdot e^{-i\textbf{S}\cdot \hat{\textbf{n}}\phi/\hbar}$$ And, then $$\psi'(\textbf{r}, m) = \langle\textbf{r}, m|e^{-i\phi(\textbf{L} + \textbf{S}) \cdot...

"However, accurate quantum-mechanical calculations (starting in the 1970s)... singly occupied orbitals are less effectively screened or shielded from the nucleus, so that such orbitals contract and electron–nucleus attraction energy becomes greater in magnitude (or decreases algebraically)."...

If you think of electrons with spin as bar magnets, you know bar magnets of opposite polarity when put next to each other in any respective rotation don't cancel each other's magnetic field out. So what's a more apt analogy for electron paired have no magnetic field?

We learn that the dimensions of spin coincide with the dimensions of other magnitudes, for example action and angular momentum. They also coincide with a purely electromagnetic dimensional form. Is the next. $$\left[spin\right] = \left[ electric \ resistance \right] \ \left[electric \ charge...

Influencing electrons angular momentum You can use magnetic fields to influence the intrinsic value of angular momentum (spin). When an electron interacts with a magnetic field it experiences a force known as torque – twisting force in the direction of the magnetic field. Therefore, if you pass...

Hi, I was reading about the EPR paradox in Bohm simplified formulation. From my understanding the paradox is that Bob is actually able to get a value for the positron's spin along both the ##z## and ##x## axes. Since electron and positron are entangled, he get the value of spin along ##z##...

Hello! I am curious about how different rotations on the Bloch sphere are done in practice. For example, assuming we start in the lower energy state of the z-axis (call it |0>), a resonant rotation on the Bloch sphere by ##\pi/2## around the x-axis will take you to ##\frac{|0>-i|1>}{\sqrt{2}}##...

We are taught that all fermions have spin ##\frac{1}{2}##, short for spin angular momentum ##\frac{\hbar}{2}##, which can be added to the orbital angular momentum. Considering spin is a kind of angular momentum, it must be dependent on the mass (or moment of inertia) of the particle. However...

Hi, I'm aware of the wave function ##\Psi## of a quantum system represents basically the "continuous components" of a quantum state (a point/vector in the infinite-dimension Hilbert space) in a basis. If we take the ##\delta(x - \bar x)## eigenfunctions as basis on Hilbert space then the wave...

how do i write the z spin state using the spin state on x or on y?

Hi Pfs, I read somewhere that if the graviton had a spin 1, then gravity would be repelling. Is there a formula showing that the attract-repel depends on the parity of the carrier's spin? thanks

and how is it known that the two photons are entangled in the first place? I mean before measuring how do you know that you have the correct two photons?

I'm trying to understand how exactly we calculate the detection rate in this specific multiple Stern-Gerlach setup. As written on the image, an (unpolarized) atomic beam is sent through a three Stern-Gerlach apparatuses, and the detector supposedly clicks 25% of the time. When I try to...

I know how position and momentum commute, but now I have the spin angular momentum operator involved as well as a dot product. Specifically, what would the commutation [x,S·p] be?

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...

Will the probability to provide a negative value of a Sz 1/2 spin system always be 0? If lambda 1 = hbar/2 and lambda 2 = -h bar/2 ?

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?

Can four (or more) electrons form a completely antisymmetric joint spin wave function？

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...