Spin Definition and 1000 Threads

How do we get (6.265)? Shouldn't we have ##exp(-i\frac{\alpha}{2}\hat{n}.\sigma)=\cos(\frac{\alpha}{2}\hat{n}.\sigma)-i\sin(\frac{\alpha}{2}\hat{n}.\sigma)##?

So far I have seen Sakurai, Townsend, Cohen Tannoudji, Feynman, and McIntyre. Are there any other books that take this approach? Just curious.

Homework Statement If an object is hanging by a thread, how fast must it be twirled around in order to break the thread? (must also provide explanation of why this is the velocity). As a part of a lab, pick a certain mass. Attach to light string (easily breaks) and pull the string through a...

I have a magnet that has a cylindrical shape, where the center is slightly larger than its outer sides. I was wondering why it beings to spin on its outer end when spun very fast (on its long edge). Whereas if its spun not too fast, it stays on its axis. I have included a photo for further...

Say we have a Helium atom with the first electron in 1s orbital and second electron in 2s orbital, and if these electrons have parallel spin so that the total spin of the system is S=1, then is this a triplet or a singlet state? According to LS coupling, multiplicity is defined as: 2S+1 (if...

Hey, I am new to the forum, and would certainly appreciate help in understanding spin - although I realize that perhaps no one really understands spin. If a beam of spin polarized electrons are absorbed in a target, then the target will start to rotate. This kind of makes sense on a...

Homework Statement Find spin only magnetic moment of ##[Fe(H2O)5NO]^{2+}## Homework Equations None The Attempt at a Solution When I used Google, the magnetic moment in 3.87 ##Fe## is in +1 oxidation state. So configuration is $$[Ar]3d^64s^1$$ There are 5 unpaired electrons. How does magnetic...

Homework Statement Hello all, Im asked to construct the state | \frac{5}{2} , \frac{3}{2} \rangle from the eigenfunctions | L, L_z\rangle and the electron states | \uparrow \rangle and | \downarrow \rangle . Homework Equations Clebsch Gordon Coefficient's table The Attempt at a...

Help. I'm really struggling with the general idea here. The intricacies of the theory are hopelessly beyond my cognitive reach. I'm just trying to get a general handle on the big picture concept. I read a bit where Lee Smolin referred to this model as a leading theory that characterized space...

The intricacies of the theory are hopelessly over my head. But I'm trying to clarify my understanding of the Spin Foam cosmological model in very basic and generalized terms. The logical starting point might be in understanding what the SPIN in spin foam refers to. My cursory scan of web...

I was wondering it the projection of the measurement axes onto a spinning vector modeled by a plane would produce correlations of entangled particles in line with what is found by experiment. Does anyone know of any discussions on this subject? Would this lead to stronger correlations than spin...

Our moon rotates around Earth in such a way that we always see the same face. But Earth orbits Sun in a different way. It keeps spinning. My question is, If I were to go to space and put a basketball in a circular orbit around Earth in such a way that at the time I throw it a particular face is...

In chapter 1 of Peskin and Schroeder, the reaction ##e^{+}e^{-}\rightarrow \mu^{+}\mu^{-}## is studied in detail. The related following paragraph is taken from page 4 of Peskin and Schroeder: Both the electron and the muon have spin ##1/2##, so their spin orientations must be specified. It is...

Hi everyone, Firstly, sorry if this seems a bit rushed, I don’t have much time in between shifts at work. You may have to refer to my links. But if needed, I will add more information later on. I've been racking my head over this for the last month or so. I’m kinda doing a private personal...

orbital movement occupy more space than spin movement. If an object are running in both orbit and spin, how to stop orbit and transfer orbit energy to spin energy? Of course the total angular momentum conserves. I know new optical technology can convert spin energy into orbital energy, but it...

Consider a system with a mirror axis (bulk projected surface), I want to know the direction of spin polarization on the mirror axis. The result is that the spin is perpendicular to the mirror axis, but I don't understand the reason. If someone have related references, please recommend to me...

Homework Statement A microwave oven operates by injecting electromagnetic waves with a frequency of 2.45 GHz into the cavity formed by the conducting metal shields on each face of the oven box. Explain, with the aid of sketches and simple calculations, why it is generally necessary to rotate...

Homework Statement Attached Homework Equations ##J_+|j,m⟩ = ћ\sqrt{j(j+1)-m(m+1)} |j,m+1⟩## ##J_-|j,m⟩ = ћ\sqrt{j(j+1)-m(m-1)} |j,m-1⟩## ##J_z|j,m⟩ = mћ |j,m⟩## ##J^2|j,m⟩ = ћ^2j(j+1) |j,m⟩## The Attempt at a Solution Hi there, For part a, the expression we're looking for is given, but...

Hello, i have to launch a ping pong ball for an engineering course. We have a system set up with two wheels spinning as fast as we can get them and a ping pong ball feeds between them and shoots. Our asignment is to create a model that shows distance shot related to the angle of launch. We also...

Just curious. Not sure if this has been discussed already, and I'm not sure what the phenomenon is called, but here's a description: I have a heavy gold class ring that I got from my alma mater. I put the ring face down on the desk, flat, and it can rest like that because the face of the ring...

In Newmann-Penrose formalism, a Null rotation with ##l## fixed is $$l^a−>l^a\\ n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\ m^a−>m^a+cl^a\\ \bar{m}^a−>\bar{m}^a+\bar{c}l^a$$ Using this transformation, how to prove? $$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$ Ref: 2-Spinors by P.O'Donell, p.no, 65

https://www.sciencenews.org/node/20378 Y'all might find this interesting. John Conway and Simon Kochen's 1-0-1 theorem. I have no questions. Sorry.

I get the notion that an elementary particle derives from a localized perturbation of that particles quantum field. What I don't get is how that perturbation can lead to two alternative quantum states for that particle - for example, an electron with two spin states (spin up and spin down). Are...

Hi buddies. I recently finished my quantum mechanics course, however, I would like to know the solution of this exercise because i couldn´t solve it on my last exam, and i would like to take this doubt off. An operator ##F## describing the interaction of two spin ##\frac{1}{2}## particles has...

Homework Statement So I have two 1/2 spin systems A and B in a singlet state |\psi > = \frac{1}{\sqrt{2}} ( |+-> - |-+> ) . The question is: If I measured B and got S_{Bz} = 1/2 . What will I measure on state A on z axis? Homework EquationsThe Attempt at a Solution The answer I think is...

Hey, guys! I was recently reading (attempting) about spin groups. I heard a little bit about SO(3), but still don't know much. I was wondering if someone could explain what a spin group is and why it is useful? Is there some way to visualize spin groups? Please note: I know literally nothing...

I have just recently started learning about quantum contextuality and can only seem to find examples where contextuality is need to explain measurements of spin. So I am curious as to whether quantum contextuality only applies to measurements of spin? Also, If someone could clarify where the...

I'm looking for a description of properties such as colour and spin. Because we are warned these words do not describe the reality of the particles. i.e. an electron is not 'spinning' up or down. They are just handy words. Labels. So quarks are not 'up' or 'down'. When I read that...

Hello, I've been reading the Stern-Gerlach experiment, and where the concept of electron spin is introduced, am facing a problem, i.e., if you consider electron a charged rotating sphere, then the electromagnetic energy and size of the electron becomes huge! So how do you deal with this? Thanks...

Hello I am joining as a Project assistant on a project called "Search for spin liquid and other novel ground states arising from an interplay between electronic correlations, spin-orbit coupling and geometric magnetic frustration" what can i read to get onto the topic for it.

Hello, just as a thought, we are used to describe spin systems of either fermions or bosons (for example, the Ising or Heisenber models, where spins are considered to be all of the same type, in both cases fermions). However, I was wondering if it makes some sense to have a system where, for...

Homework Statement Homework Equations This is a passage from Modern Quantum Mechanics by Sakurai ( page 26~27) The Attempt at a Solution I wonder how i can get 1.4.8 , 1.4.9 equations . and what do they mean?

Homework Statement [/B] Taken straight out of Szabo and Ostlund's "Quantum Chemistry" problem 2.1: Given a set of K orthonormal spatial functions, \{\psi_{i}^{\alpha}(\mathbf{r})\}, and another set of K orthonormal functions, \{\psi_{i}^{\beta}(\mathbf{r})\}, such that the first set is not...

Homework Statement Show that for a two spin 1/2 particle system, the expectation value is \langle S_{z1} S_{n2} \rangle = -\frac{\hbar^2}{4}\cos \theta when the system is prepared to be in the singlet state...

Homework Statement Find the energy levels of a spin ##s=\frac{3}{2}## particle whose Hamiltonian is given by: ##\hat{H}=\frac{a_1}{\hbar^2}(\hat{S}^2-\hat{S}_x^2-\hat{S}_y^2)-\frac{a_2}{\hbar}\hat{S}_z## where ##a_1## and ##a_2## are constants. Homework Equations In the ##\hat{S}_z## basis...

Homework Statement A beam of spin 1/2 particles with speed v passes through a series of SGz devices. The first SGz device transmits particles with Sz = ħ/2 and filters out particles with Sz=-ħ/2. The second SGz device transmits particles with Sz=-ħ/2 and filters out particles of Sz=ħ/2...

Hi everyone. I'm just looking for schematics of cnot quantum gate, but on the Internet it only talks about it from a mathematical point of view. I want to ask you if you have some drawing, or schematics of it, from a "Physical" implementation, in the sense, how are the spins prepared, how we...

Hi guys! What would happen to objects on the Earth's surface if it SLOWLY stopped spinning and Earth's gravitational field was kept as always. Thx

4rth/5th coordinate?* Hi, I'm just wondering: if there is an entity in space, which can be located with Cartesian coordinates in the 3 dimensions of say, 2 right (from a seemingly arbitrary reference point), 2 up, and 2 forwards, then at this point (2, 2, 2), an entity could also be spinning at...

This is my attempt at understanding any real world physical effects from quantum spin. I will start with the short version first. A ... When we have a free floating electron in space is the physical orientation of the quantum spin axis locked into a fixed 3D orientation and from there can only...

Hi All Thanks for welcoming me to the physics forum. I am reading Greiner and Mueller's Quantum Mechanics: Symmetries and am stuck at not understanding the vector meson ( rho meson)'s spin states. For S=1 we get three states -1, 0, and 1. Prof. Mueller separated them as a rho +/-1, and rho 0 ...

Hi, this is my first message on thi forum :D I apologize in advance for my english. I'm doing my thesis work on the theory of relativity of Einstein-Cartan. I'm following the article of Hehl of 1976; it's title is "General relativity with spin and torsion: Foundations and prospects". I can't...

I am wondering something about the tree amplitude for exchange of a spin J resonance-- the basic calculation that exhibits the famous regge behavior. I see that one way to do the calculation is simply to note that the 4-point function for spin J exchange amongst massless particles arises from an...

I'll start with this question, how much "mass" does something have to have before centrifugal force exceeds gravity on earth? I used basic physics of centrifugal force and gravity, used force vectors, and the math doesn't jive. This is what I mean. There are 2 forces on Earth that everything...

Hello everyone, In case of hydrogen atom, when we say spin up or spin down we refer to the z component of the spin. Why are we interested only in the z component of spin and not in the x and y components? Thanks in advance

So we obtain the perturbation Hamiltonian H as something proportional to S.L/r3 and the first order energy shift is then the expectation value of this perturbation Hamiltonian in the state that is being perturbed. So let a general gross structure state that we are perturbing be |n l ml s ms >...

Hello folks! New to this forum, so hoping I'm not retreading old ground. The Pauli matrices are spin angular momentum operators in quantum mechanics and thus are axial vectors. But in Clifford algebra in three dimensions they are odd basis elements and thus polar vectors. Hestenes, Baylis, other...

Homework Statement Consider the below network of spins, the spins numbered on the nodes of the diagram. The spins interact via the following Hamiltonian ##\mathcal H = \sum_{\langle i j \rangle} \sigma_i \sigma_j##, where the sum ##\langle i j \rangle## is over nearest neighbours and ##\sigma_i...

Hi, Consider model of one dimensional spin chain with a random couplings J. The Hamiltonian is the following: $$ H = \sum_i J_i (S_i^x S_{i+1}^x+ S_i^y S_{i+1}^y)$$, Which by Jordan-Wigner transformation we can transform it to the fermionic representations. $$ H = \sum_i J_j/2 (c_i...

The more detail you can see the attachment. I don't understand why Rabi translate the state along z axial to H axial as shown the equations (8).