10
votes
1answer
143 views

Can nowadays spin be described using path integrals?

In Feynmans book, "Quantum mechanics and Path Integrals" he writes in the conclusions (chapter 12-10) With regards to quantum mechanics, path integrals suffer most grievously from a serious ...
3
votes
0answers
64 views

Naive questions on the ground states of Kitaev model

Up to now, I found myself still does not have a deep understanding of the honeycomb Kitaev model, and I got some naive questions about the ground states (GSs) of the this model (with open boundary ...
0
votes
1answer
29 views

Electronic configuration for singlet and triplet states

Is there a difference in the electronic configuration for singlet and triplet states? For example, He atom has 1s2 configuration in its ground state (singlet state) But what about when the He atom is ...
1
vote
0answers
30 views

Spin with Stern gerlach Experiment [closed]

Within a week, I am trying to conduct a seminar on the topic " Spin with Stern gerlach Experiment" at my University. It would be great if you guys could provide me some inputs regarding the things I ...
3
votes
1answer
66 views

Spin-orbit coupling from the rest frame of the proton?

When we calculate the spin-orbit interaction in a Hydrogen atom we just work in the electron's frame of reference: the proton is moving and produces a magnetic field which the electron's spin ...
1
vote
1answer
49 views

Stern Gerlach with spin in opposite directions

So for the Stern-Gerlach apparatus, we assume that we either have a particle spin up or spin down. We also have the varying field, $\partial B/\partial z$. This initial configuration results in the ...
1
vote
0answers
49 views

What is conductivity?

I read that if we have spin $\frac{1}{2}$-particle, where a magetic force acts on, then the force is given by a drift speed times a conductivity. This conductivity is determined to be $\frac{kT}{D}$, ...
2
votes
0answers
32 views

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 ...
1
vote
2answers
74 views

When combining three spin $\frac{1}{2}$ particles what are the corresponding states?

I want to combine three spin half particles and this is what I have so far. I used the lowering operator $J_{-}$ on the top states and found the following states fine: ...
-1
votes
1answer
71 views

Commutator with Pauli spin matrices and the momentum operator

How is $\left[\vec\sigma \cdot \vec p, \vec \sigma \right]$ proportional to $\vec \sigma\times \vec p$, where $\sigma$ are the Pauli spin matrices and $p$ is the momentum operator?
1
vote
1answer
82 views

What is $\langle \sigma_\mu \rangle$ $\langle \sigma_\mu \rangle$ for the Pauli Matrices?

What is \begin{align} \sum_{\mu=0}^{3} \langle \sigma_{\mu} \rangle^2 = ? \end{align} $\sigma_{\mu}$ are the Pauli matrices. The Bra-Ket notation is used in this question: \begin{align} \langle ...
0
votes
0answers
26 views

Is this description of particle's spin strict?

I'm trying to understand a concept spin in QM. I've read some explainations, and it seems that the idea is very easy and straighforward, however I didn't find these exact wordings in my books. My ...
2
votes
0answers
18 views

Two identical particles with spin $s$. What is the spin of its corresponding “center-of-mass” and “relative” particles?

Consider a system of two identical quantum particles with spin $s$ and mass $m$. Using center-of-mass coordinates one obtains an equivalent system given by a particle of mass $2m$ and one of mass ...
1
vote
1answer
63 views

The Holstein-Primakoff Representation (approximation)

I have a question regarding the Holstein-Primakoff representation. In the HP-representation we define the spin operators in terms of bosonic creation and annihilation operators. $$ S_j^+ = \sqrt{2S ...
0
votes
1answer
51 views

Spin Control and Entanglement

I have a thought-experiment sort of question and I don't know where to start. Suppose you have an entangled pair, e1 and e2, and you split them. Then BEFORE reading them, you spin control e1 to +, ...
1
vote
2answers
96 views

Writing down an entanglement in bra-ket notation

I have a relatively complex (for me anyhow) situation which I would like to capture in bra-ket notation, rather than in words. However, I've not been able to find a source which will help me ...
6
votes
2answers
195 views

A paradox with spin: Is spin a physical degree of freedom?

Suppose I want to calculate the state associated with a spin particle under a magnetic field. I suppose the particle interacts via the Zeeman effect, and only through it. Then I want to resolve the ...
2
votes
0answers
40 views

Reflector Klystron and Isolator for ESR/EPR Experiment

I am doing a lab on ESR/EPR, and I would like to know how the reflector klystron operates. It is very old and the company who made our model does not exist anymore and there are no operation manuals. ...
1
vote
0answers
67 views

Can (quantum) angular momentum $L$ be zero?

I am trying to calculate the orbital magnetic moment, $\bar{\mu}$, for Sodium, which has an electron configuration of $1s^2 2s^2 2p^6 3s^1$. The full shells do not contribute to $\bar{L}$ and ...
2
votes
0answers
69 views

Free Will Theorem question

The Kochen-Specker Theorem says, if I understand it correctly, that the results of spin measurements cannot be predetermined independent of measurement. They get to this conclusion by describing 33 ...
2
votes
0answers
68 views

What are the assumptions behind “term symbols”?

In multi-electron atoms, the electronic state of the optically active "subshell" is often expressed in "term symbols" notation. I.e. $^{2S+1}L_J$. This presumes that the system of electrons has ...
1
vote
1answer
179 views

Understanding Triplet And Singlet States

We know, $2\otimes 2=3\oplus 1$. Thus we have a spin triplet of states and a spin singlet. Can we regard these states as the spin part of wavefunction for the excited states and the ground state of ...
0
votes
0answers
80 views

Diagonalize a dot product with Pauli matrices

How can I diagonalize the following operator? $$\lambda \hat{\vec{\sigma}}\cdot\vec{r}$$ where $\lambda$ is a real constant, $\hat{\vec{\sigma}}=(\hat{\sigma_{x}},\hat{\sigma_{y}},\hat{\sigma_{z}}) ...
2
votes
1answer
110 views

Are all spin states orthogonal?

For a spin 1/2 particle you have two spin states, either up or down which are orthogonal. But what about a spin 1 particle which has 3 spin states, either up, down, not up/not down?
2
votes
1answer
72 views

Spin state of electron after measurement

I have a system of two spin 1/2 particles in a superposition of spin states in the z-direction given by: $\psi = \frac{1}{2} |+ +\rangle + \frac{1}{2} |+ -\rangle + \frac{1}{\sqrt{2}} |- -\rangle$ ...
3
votes
1answer
123 views

Matrix representation angular momentum

We are supposed to give a matrix representation of $L\cdot S$ for an electron with $l=1$ and $s=\frac{1}{2}$. I read $L\cdot S$ as $L \otimes S$. Is this correct? Then we would have e.g. for ...
1
vote
1answer
76 views

Angular momentum and spin

I am having problems with this excercise. We look at a system where the total angular momentum is given by an electron with $l=1$ and $s=\frac{1}{2}$. Now I am supposed to calculate the ...
0
votes
1answer
83 views

Is there a way of measuring the spin along an arbitrary direction of a spin 1 particle?

I am familiar with the expression for spin 1/2 but haven't seen one for spin 1.
1
vote
2answers
106 views

Possible spin states?

Given a system of two particles with spin up and down, I have troubles to understand the possible states of this system. I would have normally thought, that the possible states are the tensor ...
1
vote
2answers
146 views

Which of these two different forms of spin-orbit interaction is correct?

I am seeing the spin-orbit interaction in two different ways: $\lambda [\mathbf{p} \times \nabla V]\cdot \sigma$ $\lambda [\nabla V \times \mathbf{p}]\cdot \sigma$ I don't see how these two ...
0
votes
0answers
23 views

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, ...
1
vote
1answer
125 views

Spin eigenvalues and eigenvectors problem. Is this the correct way to solve it?

An electron is described by the Hamiltonian $ H=\frac{e}{mc}\bar{S}\cdot\bar{B} $ where $\bar{S} =(S_x,S_y,S_z)$ is the spin operator and $\bar{B}$ the magnetic field. For $t>0$ ...
3
votes
3answers
82 views

At what point is the spin determined in a Stern-Gerlach Apparatus

Consider a particle with spin that travels through a Stern Gerlach box (SGB), which projects the particle’s spin onto one of the eigenstates in the $z$-direction. The SGB defines separate trajectories ...
1
vote
0answers
43 views

What are the ways of finding the spin of a particle [duplicate]

How many ways are there for this mission? Any article about that on the internet. I heard about TODAI made a reprogrammable quantum computer. Any more ideas are welcome
3
votes
1answer
159 views

Is the spin-rotation symmetry of Kitaev model $D_2$ or $Q_8$?

It is known that the Kitaev Hamiltonian and its spin-liquid ground state both break the $SU(2)$ spin-rotation symmetry. So what's the spin-rotation-symmetry group for the Kitaev model? It's obvious ...
1
vote
1answer
119 views

Is the spin 1/2 rotation matrix taken to be counterclockwise?

The spin 1/2 rotation matrix around the z-axis I worked out to be $$ e^{i\theta S_z}=\begin{pmatrix} \exp\frac{i\theta}{2}&0\\ 0&\exp\frac{-i\theta}{2}\\ \end{pmatrix} $$ Is this taken to be ...
1
vote
1answer
85 views

Addition of spin?

There is something I don't fully understand. When I have a problem like this: Let's look at a system with $j_1=1$ and $j_2=2$ spins. Let our system be in the state in which the total spin is $2$ and ...
3
votes
1answer
65 views

Did the Goudsmit-Uhlenbeck analysis of spin consider relativity?

It's frequently mentioned in introductory quantum mechanics texts that Goudsmit and Uhlenbeck conjectured that the magnetic moment of an electron was due to angular momentum arising from the electron ...
0
votes
2answers
406 views

Why can't a spin-1 particle decay into two identical spin-0 particles?

I've got this far: Suppose a spin-1 particle with $j$,$l$,$s$ decays into a system of two identical spin-0 particles with $J$,$L$,$S$. The RHS must have total spin $S=0$, so $J=L$ which must be even ...
3
votes
1answer
175 views

Nuclear Spin of Sodium 23

I am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and ...
1
vote
2answers
137 views

Some small questions about quantum spin and rotations

I'm studying about quantum-spin (in a syllabus about non-relativistic quantum-mechanics though), but I have some trouble understanding everything. So I would like to ask some small questions, which ...
3
votes
0answers
91 views

Spin Glass Prince Rupert's Drop

Spin Glass is known to converge to its ground state under Simulated Annealing. The word choice is especially interesting since annealing is also the name of a process performed on actual glass. ...
5
votes
1answer
210 views

How do I measure the spin along an arbitrary direction?

I need to measure the atoms spin along a direction perpendicular to the z-axis but at an angle $$ \phi $$ with the x-axis. They then get the output of the spin measured is + with probability $$ ...
1
vote
1answer
156 views

Spinors and Probabilities of Electron-Positron Pair

Question: An electron and positron are moving in opposite directions, and are in the spin singlet state. Two Stern-Gerlach machines are orientated in some ...
0
votes
1answer
186 views

Eigenvectors of the angular momentum operator $S_x$ [closed]

For a spin of $\frac{1}{2}$ the angular momentum operator can be written as $\vec{S} = \frac{\hbar}{2} \vec{\sigma}$ in matrix form. Find the eigenvalues and eigenvectors of $S_x$ where $\sigma_x = ...
2
votes
1answer
105 views

What is the spin state of a spin-1/2 particle when it comes out of a Stern-Gerlach apparatus?

Having a particle entering the apparatus with spin state $|+\rangle$, for which $\hat S_x|+\rangle=+\frac\hbar 2|+\rangle$, I have a question about how to express the spin state when it comes out. I ...
1
vote
0answers
45 views

Adiabatic evolution for initial Hamiltonian on Hadamard basis and problem Hamiltonian as diagonal

This is spawned from a comment at the answer to one of my previous questions. Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out ...
1
vote
1answer
57 views

Confusion about a lemma on the time constraint of an adiabatic evolution (arXiv:quant-ph/0604077)

I am going through the paper Quantum adiabatic evolutions that can't be used to design efficient algorithms by Zhaohui Wei and Mingsheng Ying. On the second page they prove a lemma. The statement goes ...
0
votes
0answers
73 views

Photons angular momentum / spin

I have a textbook that says that photons have a spin of absolute value $\hbar$ and at some other point, they say that it has angular momentum of absolute value $\hbar$. Now, since they are different ...
1
vote
1answer
74 views

Simple QM question about Sy matrix

Given a spin 1/2 particle in state $|\alpha\rangle=\begin{bmatrix}a \\b\end{bmatrix}$, what is the probability of it being measured in the $S_{y+}$ state. Is this equivalent to, if $S_y$ is measured ...