What is Spin 1/2: Definition and 106 Discussions

In quantum mechanics, spin is an intrinsic property of all elementary particles. All known fermions, the particles that constitute ordinary matter, have a spin of 1/2. The spin number describes how many symmetrical facets a particle has in one full rotation; a spin of 1/2 means that the particle must be rotated by two full turns (through 720°) before it has the same configuration as when it started.
Particles having net spin 1/2 include the proton, neutron, electron, neutrino, and quarks. The dynamics of spin-1/2 objects cannot be accurately described using classical physics; they are among the simplest systems which require quantum mechanics to describe them. As such, the study of the behavior of spin-1/2 systems forms a central part of quantum mechanics.

View More On Wikipedia.org

22. A Why are there only two possible spin-eigenstates for deuterium's nucleus?

I am studying the deuterium's nucleus. As we know, there are just two eigenstates for a spin 1/2 particle: either spin up or spin down. Thus, over the whole nucleus, you get 4 possible combinations: 1) Spin up-spin up 2) Spin up-spin down 3) Spin down-spin up 4) Spin down-spin down If you...
23. Spin Annhilation and Creator Operators Matrix Representation

Homework Statement Given the expression s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> obtain the matrix representations of s+/- for spin 1/2 in the usual basis of eigenstates of sz Homework Equations s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1> S_{+} = \hbar...
24. A Quantum synchronization description used in a paper

In the paper "Steady-state spin synchronization through the collective motion of trapped ions" it states the following: "Steady-state synchronization of atomic dipoles forms the foundation for ultra-stable optical lasers utilizing narrow-linewidth atoms coupled to a lossy cavity mode. The...
25. Ground state energy of 5 identical spin 1/2 particle

Homework Statement The ground state energy of 5 identical spin 1/2 particles which are subject to a one dimensional simple harkonic oscillator potential of frequency ω is (A) (15/2) ħω (B) (13/2) ħω (C) (1/2) ħω (D) 5ħω Homework Equations Energy of a simple harmonic oscillator potential is En...
26. Composite Spin 1/2 System Probability Question

Homework Statement Two spin ##\frac 12## particles form a composite system. Spin A is in the eigenstate ##s_z = + \frac 12## and Spin B is in the eigenstate ##s_x = + \frac 12## What is the probability that a measurement of the total spin will give the value ##0##? Homework Equations I know...
27. I Two dimenstional Heisenberg Hamiltonian for spin 1/2 system

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...
28. T

I Spin 1/2 representation of a particle

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...
29. Theoretical physics -- where does spin 1/2 come in

How did they figure out that particles have spin.where does spin 1/2 come in...how was that detected?
30. I Solving 2 Electron Spin 1/2 System: Need Help!

Hey, I am studying Spin 1/2 system, the case of 2 electrons in a magnetic field, since we have 2 electrons, we expect that the matrix will be of the size 4x4, which is what I have got. As I know that I could use the density matrix to calculate the expectation values of any physical quantity...
31. I Spin 1/2 particle emitting spin 2 particle?

As I understand it (e.g. from discussions around the Fermi field theory of the nuclear force), a spin 1/2 particle can emit a spin-1 particle and simultaneously flip its spin (say, spin +1/2 -> photon +1 & spin -1/2); but how does this work with spin-2 particles? Does it need to emit pairs in...
32. I Spin 1/2 particle confined to an infinite annular region.

Suppose we confine a spin 1/2 particle to an infinite annular region, in cylindrical coordinates, defined by the two cylinders r=a and r=b with a<b. How does such a region constrain possible spin and angular momentum? Thanks!
33. Question on spin 1/2 states in arbitrary direction

Homework Statement The problem is given above. I am struggling on the first two parts, where I am tasked with finding gamma and beta. Homework Equations For spin one half states in arbitrary directions, I know that psi = a*|n;+> + b*|n;-> . |n;+> = cos(theta/2)|+> +sin(theta/2)*ei*phi|->...
34. Interaction of Two Spin 1/2 Particles

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...
35. Spin 1/2 systemin Sakurai quantum mechanics

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?
36. Expectation value of spin 1/2 particles along different axes

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...
37. Superposition of states, spin 1/2

Homework Statement Two particles, their spin are 1/2. The hamiltonian is ##H=\gamma s_1 \cdot s_2## At t=0, the state ##|\alpha(0)>## is such as ##s_{1z}|\alpha(0)>=\hbar/2 |\alpha(0)>## and ##s_{2z}|\alpha(0)>=\hbar/2 |\alpha(0)>##. Find the state ##|\alpha(0)>##.2. The attempt at a...
38. Is the Energy of a Spin 1/2 Particle Always Equal to h/2?

We know Sz = h/2 [1 0 // 0 -1] for up spin.So can we say that the energy of the electron in this state is h/2 ? (since Sz |up> = h/2 |up>)Now we consider a Hamiltonian H = [1 0 // 0 -1] which has eigen values +1, -1 and the respective states are (1 0) and (0 1). If we see the...
39. Spin 1/2 Particle: Uncertainty Principle Explained

In my book (Griffiths) it is said : A particle is in ↑ state. The z-component of the particle's spin angular momentum [Sz] is h bar/2. The x- component of the particle's spin angular momentum [Sx] can be either h bar/2 or...
40. Eigenstates of 3 spin 1/2 particles

Hi, I have learned about how to find the 4 spin states of 2 spin 1/2 particles, and how to find them by using the lowering operator twice on |1/2, 1/2> to find the triplet, then simply finding the orthogonal singlet state, |0, 0>. I started to attempt finding the states of 3 spin 1/2...
41. Question of spin 1/2 particles in a rotating field

Homework Statement So I'm given a spin 1/2 particle in a rotating magnetic field in the (x,y) direction and a constant field, B_0, in the z direction and am asked to find the S matrix describing it. Given is: B(t) = [B_1 \cos(\omega t), B_1 \sin(\omega t), B_0] Homework Equations H = \sum...
42. Spin 1/2 - Is √3/2ħ or √¾ħ Correct?

Hi, I was looking at the wikipedia article for spin 1/2 http://en.wikipedia.org/wiki/Spin-%C2%BD and it stated that √(½(½+1))ħ=√3/2ħ. According to my math it is √¾ħ. Is this just a typo or am I missing something?
43. Are there separate quantum fields for spin 1/2 particles in modern QFT?

The spin observable for spin 1/2 particles is represented by Pauli Matrices acting upon a 2-dimensional Hilbert Space. In RQM, forgetting about the matter-antimatter duality for the moment, that TWO-state Hilbert Space is directly related, through the Lorentz Group, to the TWO separate...
44. Density Matrix for Spin 1/2 particle in a magnetic field

Hi everyone! I am trying to create the density matrix for a spin-1/2 particle that is in thermal equilibrium at temperature T, and in a constant magnetic field oriented in the x-direction. This is a fairly straightforward process, but I'm getting stuck on one little part. Before starting I...
45. What does a spin 1/2 wave function actually look like

I have only ever seen the wavefunction for a spin 1/2 particle written in the basis set |α> |β>. I was interested in how a wavefunction |ψ> = a|α> + b|β> might be rewritten in a continuous basis and hence would need to know what the actual functions of |α> & |β> were. Thanks
46. Two identical particles with spin 1/2

hello guys , in this problem from zettili quantum mechanics that i attach , i think something is wrong , first the problem said two particles with spin 1/2 but didn't mention that the system is in singlet state or triplet state , so if the system be in triplet state then our spatial wave...
47. Spin 1/2 System: Eigenstates of Sz and Probability of Measurement

Homework Statement For a spin 1/2 system, the eigenstates of z-component of the angular-momentum operator Sz are given by: S_z |\pm> = \pm \frac{\hbar}{2}|\pm> Suppose at time t, the state of the system is given by: |\psi> = a|+> + b|-> If Sz is measured, what are the possible results of...
48. Degenerate Perturbation Theory: Two Spin 1/2 Particles

So I know this might be a lot to read but I am having a very hard time understanding how to use the formulas in degenerate perturbation theory. Here is the problem I am on. Homework Statement A system of two spin-1/2 particles is described by the following Hamiltonian...
49. Proof that a Dirac particle has spin 1/2?

Hi, I am having trouble following the Peskin and Schroeder and their derivations to show that a Dirac particle is a spin 1/2 particle (page 60 and 61). I understand how he gets the first (unnumbered) equation on page 61. However, I don't understand how he gets to the second equation...
50. Basic Probability question for a spin 1/2 Particle

Homework Statement A beam of spin-1/2 particles is prepared in the state \left|\psi\right\rangle=\frac{2}{\sqrt{13}}\left|+\right\rangle_x+i \frac{2}{\sqrt{13}}\left|-\right\rangle_x ￼￼￼￼a) What are the possible results of a measurement of the spin component Sz, and with what probabilities...