Spin 1/2 Definition and 109 Threads

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...

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...

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...

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...

Homework Statement "A spin 1/2 electron in a hydrogen atom is placed in a time-independent magnetic field B=B0(k) The electron's spin starts in the |z+> state at t=0. Calculate probability o ffinding the electron in the |y-> state as a function of time for t>0. Homework Equations...

Homework Statement Homework Equations The Attempt at a Solution To be honest I'm clueless. I've missed a large amount of the course and just struggling to find any sources that explain this. I don't want the answer to the question, I want to figure that out for myself. What I really need is...

I'm learning about NMR and it's been stated that deuteron has a spin 1 nucleus and so should exhibit different behavior. Why? I've heard of electrons having spin, and now protons, but I don't see why the spin of a neutron should matter since it's uncharged. I'm thinking a spin of 1 means...

This has been a contradiction in my brain for some time. If I want to rotate one nuclei (spin 1/2), with say an applied magnetic field B and RF pulse (at the appropriate larmor frequency), how does the spin actually rotate? I thought it can only take on discrete values of 1/2 or -1/2...

What's a pin 1/2? How can one spin 2 whole revolution to get to the same side? I don't get it. How about spin 0,1,or 2. What do those mean?

Homework Statement consider the possible angular momentum states |s,m>, of a system of two spin-1/2 particles construct all possible states with total spin zero (S=0) Homework Equations The Attempt at a Solution if total S of system is zero, m must also equal zero. So the...

Dear Forum, I would like to understand what the origin of spin 1/2 is. I read in Feynman's lectures that the origin is related to quantum field theory. I know nothing about quantum field theory. Is there an easy explanation? Thanks Cabrera

Homework Statement two identical particles of spin 1/2 that confined in a cubical box of side L. find the energy and wave function (non-interacting between particles) Homework Equations for a cubic boxby and reducing the Schrodinger equation: ψ(x,y,z)=√(8/L3 ) sin((nx πx)/L)sin((ny...

Hi, Everybody! Currently, I am reading the book "Lectures on Quantum Field Theory" (by Ashok Das) But I am a bit confusing. Why does Dirac Equation describe spin 1/2 particles? I have already known that Dirac Equation bears some angular momentum structure, but why it just describe spin...

I think I have a pretty good handle on how scalar field scattering works in QFT, so now I'm trying to wrap my head around spin 1/2 particles, and I'm having a bit of trouble with it. For instance, in N + \phi \rightarrow N + \phi scattering, an application of the Feynman rules leads to an...

Dear forumers, I was thinking about how the Sz operator "couples" (has non zero matrix elements) states with the same expectation values for the projection of spin on the z-axis (duh! α and β are its eigenvectors), and how Sx and Sy couple different states (once again, duh!). I was also...

Hello all, Imagine two spin 1/2 particles that are entangled, going towards two stern-gerlach apparatuses, with some relative angle. Now imagine one stern-gerlach device measures the spin of one of the particles as up. What is the chance that the other stern-gerlach device measures the spin...

Hello everybody, I was watching a lecture on quantum mechanics, and the lecturer was talking about the 720 degree rotation required for a spin 1/2 particle to return to an identical state. I'm aware of this, but I was more interested in the experiment to show that there is an actual...

So this is my first quantum mechanics class and so far we have spent about a month (well 3 weeks) on just the mathematics. So in my book, the author explores the ideas presented by the stern gerlach experiment. It related the beam of silver atoms traveling through the separators to light...

this sounds like a question that should be answered somewhere, but i can't find it. how many quantum numbers does it take to specify the state of a spin 1/2? 1. if it points along z, then just 1: the eigenvalue of Sz will do (up to global phase) A. whether or not in a B field B. if...

Homework Statement This is from my first-quarter graduate QM course. Part 4 of this problem asks me to compute the unitary operator U which transforms Sn into Sz, where Sn is the spin operator for spin 1/2 quantized along some arbitrary axis n = icos\phisinθ + jsin\phisinθ + zcosθ.Homework...

explicit form for representing "two spin 1/2 system" Hello, Are there any explicit forms(functions) for representing a "two spin(1/2) particle system" whose states are "proton1 up / proton2 up", "proton1 up / proton2 down", "proton1 down / proton2 up", "proton1 down / proton2 down"? Can it...

Why is there no gauge symmetry for spin-1/2 fields? Has gauge symmetry to be related to spin-1 fields/ particles? thanks

Homework Statement Two spin 1/2 particles interact through the spin-dependent potential V(r)=V_1(r)+V_2(r) \sigma ^{(1)} \cdot \sigma^{(2)} Show that the equation determining the bound states can be split into two equations, one having the effective potential V_1(r)+V_2(2) and the other...

Hi, I'm doing question 2/II/32D at the top of page 68 here (http://www.maths.cam.ac.uk/undergrad/pastpapers/2005/Part_2/list_II.pdf ). I have done everything except for the last sentence of the question. This is what I have attempted so far: |\chi\rangle=|\uparrow\rangle=\left(...

How do we show that the state |\chi>=\frac{1}{\sqrt{2}}(|\uparrow>|\downarrow>-|\downarrow>|\uparrow>) has total spin zero? Does it involve acting some combination of the spin operators on it? I know that the total spin operator \underline{S^2}=S_x^2+S_y^2+S_z^2=\frac{3\hbar^2}{4}I where I...

How did they get (u,v) in the second line and then alpha+? http://i111.photobucket.com/albums/n149/camarolt4z28/2010-11-20113911.jpg?t=1290274889

Hi, Why would having \partial\psi\partial\psi lead to a Hamiltonian that is unbounded below? Srednicki states that in order to have a bounded Hamiltonian one must include \psi^{\dag} in the combination too. Also why exactly do we require or Lagrangian to be Hermitian, is this somehow to...

spin 1/2 placed in a magnetic field at x-direction Hello guys I have been a regular reader of this forum. This is my first thread. Homework Statement A spin-1/2 is place in a magnetic field which points in the x-direction. The Hamiltonian is \hat{H} = - B Sx where Sx = h/2 * pauli...

Homework Statement How does the wave function of spin 1/2 change under parity? Homework Equations The Attempt at a Solution The behavior of the eigenfunctions of orbital angular momentum L is easily seen from their explicit form, namely spherical function Yml is multiplied by...

Hi, for my quantum mechanics course I'm confronted with the following question: Homework Statement A spin 1/2 particle has the following eigenstates of Sz: |+> = (1 0) and |-> = (0 1). A magnetic field is pointing in the z direction, B = (0,0,B). The Hamiltonian is H = -B * n, with n =...

Hi, I have this article in which I saw that for a spin 1/2 particle confined to move along a ring positiond in a magnetic field with a z and \varphi The Hamiltonian is given by: (in second attacment) What I do not understand is how do you get the last term in the Hamiltonian. Any help...

Homework Statement three distiguishable spin 1/2 particles interact via H = \lamda ( S_1 \cdot S_2 + S_2 \cdot S_3 + S_3 \cdot S_1 ) a) What is the demension of the hilbert space? b) Express H in terms of J^2 where J = S_1 + S_2 + S_3 c) I then need to find the energy and...

Here is the problem: How can relate the magnetic field and the rotations and then the length of the area? I only know that 2pi rotation give the initial state a pi phase but that's all. where the hell I get the length from? thanks

Hi everyone, A QM question that I am stuck on: Consider the addition of the spin of 2 electrons, s1=s2=½. Show that there are one ms=1; two ms=0 and one ms=-1 states. Show the 4 spin states are given by: a1a2 b1b2 (1/(sqrt(2)))(a1b2+b1a2) (1/(sqrt(2)))(a1b2-b1a2) I've used a...

Temperature in a nuclear spin 1/2 system?? Homework Statement A solid at temperature T contains 10^20 protons which have a spin I = 1/2 and a nuclear g-factor of 5.59. Calculate the temperature such that 75% of the protons have their magnetic dipole moment aligned parallel to the applied...

I was told that if you put a spin 1/2 particle in a magnetic field, it will align with or against the field. But some places it also says that it will precess around the field. Which one is right?

Why there can exist some particles having spin = 1/2? I understand, the postive numbers but what do the negative number mean? Also, I would like to ask why some photons can be detected when it comes to light, but photon is not detected when it comes to charge replusion? What is the difference...

I wanted to ask if there is any connection between the SU(2) group for the spin 1/2 and the gauge group of weak interactions. I feel there isn't much of a connection other than the fact that they share the same group properties, but I am not sure. Thanks to anyone in advance that can clarify...

First, this is my 1st post on physicsforums.com, so I'm not too sure I'm posting this in the right place, but guts tell me this is a good place to start. Second I'm sure you've all heard this question a million times. I've seen it answered here a couple of times, but what I've seen is of no...

Hi: I am confused that we talk in general about only nuclear spin larger than 1/2 which has electric quadrupole. For spin half, there is no quadrupole because of its spherical shape. Anyone can comment on why they are sphere? what is physical significance behind? I read some research articles...

Homework Statement Hi all. I'm reading about spin 1/2, and I am having a hard time understanding it. I hope you guys can fill the gaps. Here is where I stand at the moment: The basis vectors are "spin up" and "spin down" in the direction of the z-axis. Thus we have for spin 1/2 in the...

1. 1) Consider a spin 1/2 system... a) write expressions for the operators Sx Sy Sz in the basis composed of eigenkets of Sz b) Write eigenvalues of Sx Sy Sz c) Write eigenvectors of Sx and Sy in this basis 2) Write a matric corresponding to the operator S_ in the basis composed of the...

Homework Statement Given two identical, interacting spin 1/2 particles in 1D the Hamiltonian is: H = (p1)^2/2m + (p2)^2/2m + (mw/2)*(x1-x2)^2(a) Determine the energy spectrum. (b) Determine the corresponding eigenfunctions including spin state. The Attempt at a Solution I feel like I've...

Homework Statement See pdf file: http://www.2shared.com/file/3469465/52e02653/q3_online.html Its the third problem I'm having trouble with. I'm pretty sure I have the two first questions correct. Homework Equations...

The way I am being taught in my course is that instead of !s_1= 1/2, m_1 =1/2 ; s_2= 1/2, m_2 =1/2 > = !+ + > !s_1= 1/2, m_1 =1/2 ; s_2= 1/2, m_2 =-1/2 > = !+ - > !s_1= 1/2, m_1 =-1/2 ; s_2= 1/2, m_2 =1/2 > = !- + > !s_1= 1/2, m_1 =-1/2 ; s_2= 1/2, m_2 =-1/2 > = !- - > We have...

Hi all, Can anybody please explain to me the connection between Rabi oscillations and spin-1/2 systems? I believe the connection lies in the bloch sphere and the ability to represent the spin-1/2 system by a superposition of Pauli matrices but I'm just not getting it. Thanks

As mentionned in the "A question about nonlocality" thread, the electron (a spin 1/2 particle) must turn twice to be back in its original position (so that its complex wave function is identically restore). Now my question is this: If a spin 1/2 particle must turn 2*360 for it's wave...

[SOLVED] Addition of Spin 1/2 Homework Statement A system is composed of two spin 1/2. The system's hamiltonian is H=w_1 S_1z + w_2 S_2z. The initial state of the system is, at t=0, | \psi (0) > = \frac{1}{\sqrt(2)}[|+ -> + |-+>] . a) At time t, we measure S^2 = (S1+S2)^2 What...

Homework Statement Consider a spin 1/2 particle placed in a magnetic field \vec{B_0} with components: B_x = \frac{1}{\sqrt{2}} B_0 B_y = 0 B_z = \frac{1}{\sqrt{2}} B_0 a) Calculate the matrix representing, in the {| + >, | - >} basis, the operator H, the Hamiltonian of the...

Hello, I need help understanding spin 1/2 particles and writing down expressions for the amplitidues of spin up/down states as a function of time. Any help is appreciated or links to other information. Thanks!