===== Nov 20 (Fri) Spin and magnetic fields: Larmor precession, S-G ===== **Return to Q&A main page: [[Q_A]]**\\ **Q&A for the previous lecture: [[Q_A_1118]]**\\ **Q&A for the next lecture: [[Q_A_1123]]** **If you want to see lecture notes, click [[lec_notes]]** **Main class wiki page: ** [[home]] --------------------------------------- ==== joh04684 11/19/09, 3pm ==== I've got a quick question on the Stern-Gerlach experiment. On page 182 in the description of it, it says that we would normally expect a "smearing" of the two lines that are deflected, but instead we just see two perfect lines...Do they expect it to blur because of the uncertainty princible such that we know the angular momentum in the z direction of the beams leaving, so the actual position of the parts of the beam shouldn't be known as well? The way I read it, they say the reason there isn't any smearing is because the angular momentum is quantized. Wouldn't this pose a problem for the uncertainty principle then, if we can get around the predicted "smearing" by giving it special quantized values, or am I just misunderstanding this? ===Pluto 4ever 11/19 5:20PM=== From what I get about this, the smearing is predicted in terms of classical mechanics. This would be a result of the particles corresponding to each individual value for the m quantum number. However, in quantum mechanics we know that each particle has some manner of spin to it thus each particle is quantized in the z direction. As Yuichi showed us in class, whether they have spin up or spin down rotations determines whether they deflect up or down. === prest121 11/19/09 6:15 pm === It would be smeared if the particles could have any value for their spin. The spin value determines how much the particle is deflected by the magnetic field. Since the spin is only 1/2 or -1/2, there are only two deflections that the particles could have. === joh04684 11/20/09 10:51 am === Oh okay thanks, that clears things up for me! ====David Hilbert's Hat 11/19/09 11pm==== Why can you ignore the x component of the magnetic field in the Stern-Gerlach experiment? Griffiths mentions that it is because of the Lamor precession about B0, but what does this mean? === joh04684 11/120/09 11am === You can ignore the x-componenet because, since the Laromar precession is going around in that direction, it averages to zero so there is no net field in the x direction, only in the z-direction. ====Daniel Faraday 11/20 1030am==== I am still confused about all the different, equivalent(?) terminology we used on Wednesday to describe spin eigenfunctions. Can someone explain what they mean and/or how it is that they are equivalent to each other? ===Devlin=== I'm confused by this as well. ===David Hilbert's Hat 11/20 11am=== Do you mean the spinors or the | s m> , | s (m +1)> business? Because I was pretty lost when writing things like S | s m > on what the ket means, but if you go back to chapter 3 it says that any ket is a vector in Hilbert (!) space, so it must correspond to a particle having a generic spin s and associated m. When you operate on it with the different S operators, the eigenvalues are your observable spin states. If you look in the book Griffiths never actually writes down explicitly what any operator or state is for spin, because you can use commutation relations to find eigenvalues instead of solving a more difficult problem involving operators and states. ==Pluto 4ever 11/20 6:30PM== I was also confused about this as well. Thanks for the input. Now maybe I'll be able to do problem 18 in the homework. ====Jake22 11/22 8:10pm==== We have seen examples of the nature of coupling between spin and electromagnetic interactions (Stern-Gerlach). For example we know that any charged particle with spin also has a magnetic moment. What can we say about the nature of coupling between spin and strong or weak interactions? ====Blackbox 11/23 11am ==== Can you explain the meaning of (1) and (2) of S = S^{(1)}+S^{(2)} on page 184. ===Jake22 11/23 3:50pm === They are referring to particles 1 and 2, respectively. ====ice IX 11/23 18:44==== On page 182 Griffiths discusses the Stern-Gerlach experiment, and uses the specific case of the silver atom to show that the net spin is s=1/2. This net spin comes from the unpaired valence electron. What happens when the valence contains a pair (or pairs) of electrons, but no unpaired electrons? Will there be no beam splitting in such a situation? ====Jake22 11/30 18:34==== In the Stern-Gerlach experiment, why must we have a beam of relatively heavy atoms in order to construct localized wave packets and treat the motion in terms of classical particle trajectories? How heavy must they be? === Blackbox 19:10 === The experiment can be used to demonstrate that electrons and atoms have intrinsically quantum properties, and how measurement in quantum mechanics affects the system being measured. I think that the purpose of relatively heavy atoms are to prevent the gross deflection of the orbit of a charged particle in a magnetic field and bring out the spin-dependent effect. --------------------------------------- **Return to Q&A main page: [[Q_A]]**\\ **Q&A for the previous lecture: [[Q_A_1118]]**\\ **Q&A for the next lecture: [[Q_A_1123]]**