Spin Definition and 1000 Threads

Hello! I want to make sure I understand the relation between this and rotation (mainly between SU(2) and SO(3), but also in general). Also, I am a physics major, so I apologize if my statements are not very rigorous, but I want to make sure I understand the basic underlying concepts. So SU(2) is...

Homework Statement (a) If a particle is in the spin state ## χ = 1/5 \begin{pmatrix} i \\ 3 \\ \end{pmatrix} ## , calculate the expectation value <Sy>(b) If you measured the observable Sy on the particle in spin state given in (a), what values might you get and what is the probability of...

Why is it that bosons (particles having symmetric wave functions) have integral spins and fermions (particles having antisymmetric wave functions) have half integral spins? A lot of books state this without specifying the reason. I was wondering if this is a theoretical deduction. Or is it an...

Homework Statement Find the normalised eigenspinors and eigenvalues of the spin operator Sy for a spin 1⁄2 particle If X+ and X- represent the normalised eigenspinors of the operator Sy, show that X+ and X- are orthogonal. Homework Equations det | Sy - λI | = 0 Sy = ## ħ/2 \begin{bmatrix} 0...

I tried to answer it and got 3/4 or 6/8 after using the union set operation for 4/8 or 1/2 and 3/8, based on what is being asked in the problem...

Hello! I am a bit confused about the idea of spin. Let's say we have spin ##1/2## particles. This means that the spin along a random axis is ##\pm 1/2##, right while the values of the particle spin (i.e. the module) is actually ##\sqrt{1/2(1+1/2)}##? Also I am a bit confused about combining...

I have read in the internet that "One naturally derive the dirac equation when starting from the relativistic expression of kinetic energy: ##\mathbf H^2=c^2\mathbf P^2 +m^2c^4## where ##\mathbf P## is the canonical momentum. Inclusion of electric and magnetic potentials ##\phi## and ##A## by...

Hey everybody, I am trying to expand a system of seven qubits from one dimensional Hamiltonian to the two dimensional representation. I have the one dimensional representation and I don't know what to add to transform it from 1D to 2D representation. I would really appreciate your help and...

I am a bit confused about spin conservation at relativistic energies. I am reading a QFT book by Peskin and at a point he specifies that "In the nonrelativistic limit the total spin of the system is conserved". Later when we go to the relativistic limit (there is the interaction between a photon...

Can momentum space also able to handle spin and polarizations? I'm understanding it that in QM, you have position, momentum, spin, polarization as observables. Position and momentum can be equivalent via Fourier transform. So if you use momentum space instead of position, how do you handle...

There's enough angular momentum in electron spin to get a 1cm radius ring of silver atoms to turn with a period of order days after relaxing from spin-up into randomness. (assuming you could get all of it to show up externally, and not end up in microscopic rotations or l quantum numbers.) I...

I am currently reading Leonard Susskind's "Quantum Mechanics the Theoretical Minimum". In chapter 2.3 and 2.4, he defines |r>, |l> and|i>, |o>, for r and l along the x-axis and i and o along the y axis. The equations are: $$|r> = \frac{1}{\sqrt{2}}|u>+\frac{1}{\sqrt{2}}|d>$$ Since...

Homework Statement After beta- decay electron and antineutrino comes out, electron is moving along z axis and it is moving with velocity v. It's spinor is ## \mid\chi\rangle=A\left(\frac{\sqrt{1+\frac{v}{c}}\sin\frac{\theta}{2}}{\sqrt{1-\frac{v}{c}}\cos\frac{\theta}{2}}\right) ## where A is...

Hi, I have been trying to understand how the spin hall effect comes about. However, everywhere I look I just find 'the spin-orbit interaction couples the charge and spin current'. I really don't understand how does the current couple through the interaction. Any help would be much appreciated...

Homework Statement A wheel is spun up from rest by application of a force applied to the rim of the wheel. Consider the wheel to be in the plane of the paper, rotating clockwise. This force must point in what direction. 1) at the bottom of the wheel, pointing right 2)at the top, pointing left...

Hello, I am learning about Excited states of Helium in my undergrad course. I was wondering if the total spin operator Ŝ is a vector quantity or not. Thanks for your help.

Homework Statement Hi all, here's the problem I need help with: Compare the following situations : A beam of atoms has half of them preselected having spin up along z and the other half having spin down along z. This beam is sent through a Stern-Gerlach (SG) apparatus that sorts in the z...

Homework Statement The Hamiltonian of the positronium atom in the ##1S## state in a magnetic field ##B## along the ##z##-axis is to good approximation, $$H=AS_1\cdot S_2+\frac{eB}{mc}(S_{1z}-S_{2z}).$$ Using the coupled representation in which ##S^2=(S_1+S_2)^2##, and ##S_z=S_{1z}+S_{2z}## are...

Hi, I'm recently learning the Dirac equation and we're following the more historical approaching working in the Dirac basis. At first it seems OK that the upper two components are interpreted as positive energy and the lower two negative. However, when I learned that after a boost the spinor...

I have some serious issues trying to understand the idea of the spin in the context of the Stern-Gerlach experiment and would appreciate some assistance! Assuming that a homogenous magnetic field ##B## in the "North-wards" ##z##-direction, assume that there is a magnetic dipole moment ##\mu##...

It is well established that Fermionic or quantum spin is described by the Pauli matrices and their algebra which give the basis vectors and operators. Consider a superposition of spin-up and spin-down states ##\psi_S = \cos(\alpha)|z_+\rangle + \sin(\alpha)|z_-\rangle## and project into...

Homework Statement Consider a solid spinning sphere of negative charge in a non-uniform magnetic field: http://d2vlcm61l7u1fs.cloudfront.net/media%2F2f8%2F2f840122-3d7f-4af3-98a7-efa9b2e7d26a%2FphpBOhfaK.png (the rotation illustrated at the top is supposed to be counter-clockwise). What...

I am to try to find simple way to spin a spinning flywheel. What linear motion device acting on the outside edge of a spinning flywheel can be used to increase the speed of the flywheel. Need to use a repeating pattern such as pushing your hand down over and over on the edge of the wheel to...

I'm not at all involved in QG but from far away I noticed : Spin 2 representations are 5x5 matrices. But in gravity what mathematical objects are quantized ? If it's the metric then it's a 4x4 matrix so that cannot be that. Or : how does quantization reveal a 5x5 matrix ?

Can anyone explain to me why angular momentum of F-19 equals to J=1/2, but if we calculate J with the shell model the result is J=5/2. Thank you

The following matrix A is, \begin{equation} A= \begin{bmatrix} a+b-\sigma\cdot p & -x_1 \\ x_2 & a-b-\sigma\cdot p \end{bmatrix} \end{equation} The inversion of matrix A is, \begin{equation} A^{-1}= \frac{\begin{bmatrix} a-b-\sigma\cdot p & x_1 \\ -x_2 & a+b-\sigma\cdot p...

I’ve been watching the Susskind lectures on utube and already confused. Measurement of spin in up state gives up ( in sig z) while measurement of down gives minus down. What experimentally is the difference between down and minus down? Gf

Please excuse me if it's not appropriate to post this question here, but since this group has knowledge of both math and snooker... I'm wanting to make my own "measles ball" for practicing spin on the cue ball. These are cue balls with 6 dots perfectly/evenly spaced on the ball so you can see...

Hi I'm recently reading something about the moller scattering in QED, and I'm feeling a bit curious about how plane waves change their spin orientations (e.g. up to down)(I mean in the scenario that one is up and one is down). In the text it seems that it's because the electrons are...

Homework Statement Given 3 spins, #1 and #3 are spin-1/2 and #2 is spin-1. The particles have spin operators ## \vec{S}_i, i=1,2,3 ##. The particles are fixed in space. Let ## \vec{S} = \vec{S}_1 + \vec{S}_2 + \vec{S}_3 ## be the total spin operator for the particles. (ii) Find the eigenvalues...

Homework Statement Consider a system A consisting of a spin 1/2 having magnetic moment ##\mu_0##, and another system A' consisting of 3 spins 1/2 each having magnetic moment ##\mu_0##. Both systems are located in the same magnetic field B . The systems are placed in contact with each other so...

Homework Statement The Hamiltonian of a spin 1/2 particle is given by: $$H=g\overrightarrow { S }\cdot \overrightarrow { B } $$ where ##\overrightarrow { S }=\hbar \overrightarrow{\sigma }/2## is the spin operator and ##\overrightarrow { B }## is an external magnetic field. 1. Determine...

I'm reading about the theory behind MRI, specifically from Farr's Physics for Medical Imaging, 2nd Edition, by Allisy-Roberts and Williams. According to this book, the spins of the free protons in a sample line up, either parallel or antiparallel, with the externally applied magnetic field. In...

I don't care whether it goes clockwise or anticlockwise so this is not the usual Coriolis conversation. Why doesn't it just go down straight?

Homework Statement So given XXh chain: $$\hat{H} = -J \sum ( S^x_j S^x_{j+1} +S^y_j S^y_{j+1}) + h \sum S^z_j $$ Requred to find $$\langle g| S^z_{j} S^z_{j+n} | g \rangle$$, where g is ground state. 2. The attempt at a solution Using Jordan-Wigner transform firstly I abtain: $$\hat{H} =...

Pulsars are known to rotate at very predictable frequencies. If a beep or short tone is assigned to each rotation, the spin of the star can be 'sonified'. Pulsars spin anywhere from a few fractions of times per second to over 600 per second. 600 cycles is audible in the human range of hearing...

I'm looking into chemical battery that use the molecular tension in chemicals like white phosphorus to store heat energy.But finding a way to slow and defuse the heat and flammability of phosphorus with tungsten and sliver is easy. But rebuilding the molecular tension is harder.

Hello, I have found the technology of spintronics very interesting with a great potential for the (hopefully near) future & I am desiring to experiment with spin waves. I am sure there are several ways to create a spin wave or current, one of which involves placing a platinum strip at the end...

The helicity in non relativistic quantum mechanics is given by ##\sigma \cdot p / |p|## where ##\sigma## are the pauli matrices and ##p## the momentum. In spinor space, the ##\sigma## are 2x2 matrices, and thus, the helicity, if we calculate it, is a 2x2 quantity. But in 3d physical space, the...

The picture shows an experimental setup where one or more silver atoms are sent from an oven through 3 Stern-Gerlag (SG) filters with outputs from E and F going to detectors. If C and D remain coherent they can recombine to restore the original state and the particles all go through port E. If...

A spin 1/2 particle is represented by a spinor while its position is represented by a three-vector. What object should we use to represent such particle if we want to consider both features? That is, what object should we use if we want to consider both spin and space position? It seems there's...

< Mentor Note -- Poster has been reminded to post links in future thread starts to help others understand the question being asked > Since SWIFT gliders do not have tails, what stops them from going into forward/backward spin ?

Homework Statement Homework Equations This is the way to solve when magnetic field B is arbitrary direction one. The Attempt at a Solution I got a eigenvalue of this Hamiltonian and eigenstates. but i have no idea how to set a coordinate to value the gradient

What is the interpretation of the fact that photons have spin zero? Does it has do to with the fact that their proper time variation is zero? Or let's go a bit deeper into the math. If it's possible to write down an eigenvalue equation for photons as it is possible for electrons, then we should...

Homework Statement 1. Homework Statement The Earth turns once around its axis in 24.0 hours. We will assume that it is perfectly spherical, with radius 6400 km. The mass of the Earth is taken to be 6.00 × 1024 kg. The gravitational acceleration on the surface is taken to be g = 9.80 m/s2 . a)...

How do we experimentally apply the operator ## \exp{\left(-i\phi\frac{ S_z}{\hbar}\right)}## on a quantum mechanical system? (Here ##S_z## is the spin angular momentum operator along the z-axis) For example, on a beam of electrons?

In an Elastic Collision in free space with no gravity or friction of two solid balls of radius r1 and r2 I need to calculate the momentum and kinetic energy of the induced spin with angular velocity w1 and w2 to solve for the Conservation of Momentum and Kinetic Energy. Spin Angular Velocity w1...

I'm studying for a qualifying exam and I see something very strange in the answer key to one of the problems from a past qualifying exam. It appears the sigma^2 for a two electron system has eigenvalues according to the picture below of 4s(s+1) while from my understand of Sakurai it should have...

In an electric motor, there exists two magnetic fields where usually one of them is a permanent magnet whilst the other is an electromagnet. However, how does the magnetic fields enable the armature to rotate / spin? Also, how is the torque from the rotation of the armature transmitted to drive...

Is the beam of a pulsar projected perpendicular to its spin? If so, is the "pulse" due to wobble?