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 Jan 7 comment Which of these two different forms of spin-orbit interaction is correct? but $\vec{p}$ is also an operator and proportional to $\vec{\nabla}$. So I would expect your RHS to be 0 (curl of grad is zero). Oct 14 comment Wave functions for 2D potential with spin interactions yes. If it makes more sense, I am thinking of this as a scattering problem. An electron is elastically scattering from the above potential. Sep 24 comment Do spin-spin interactions break time reversal symmetry? @Timrok, I see your point. In this paper, the opposite is assumed: arxiv.org/abs/1304.5096 Sep 24 comment Why the name “optical phonon”? why couldn't the atoms in a one-type-of-atom solid move out of phase also? Wouldn't those be optical phonons also? Apr 6 comment how to solve this scaling equation Sorry for being difficult but I am not able to get the ansatz from your final final equation. I am subbing in $x = log s - log b$. Is this type of scaling equation covered in any textbooks? Apr 5 comment how to solve this scaling equation thanks for the answer. The problem is tougher than I envisioned. I'm still working through what you wrote and I wasn't clear what your $f(x)$ is. Is that the same as $\psi$? Also it seems that s/b would shift x by -log b. Oct 18 comment electron hole exchange I figured it must have been something along those line. Any idea where I could learn more about this? Aug 31 comment Where can a good treatment of the 'sudden' perturbation approximation be found? Thanks for the suggestion. It has been translated to English and is on Amazon. Just ordered it from the library. Aug 14 comment parallel/anti-parallel vs. triplet/singlet description of two spins Here is my problem then. Consider a single spin $\uparrow$ at a site. Now bring in another spin. In the first basis you write, there is a 50 % that the added spin can coexist at the site since there is a 50 % chance it will be anti-parallel (so by Pauli exclusion). In the second basis, it would be a 75 % chance they could exist on the same site since there is a 75 % chance they will form triplet state. Where am I wrong here? Jun 25 comment generalizing spin rotations Thanks @PeterMorgan. Yes, I see now that the type of operator would be important. I am thinking of two spins so the matrix would be another spin operator so $\vec{S} \cdot \vec{I}$ where S and I commute but the eigenvalues would not be +/-1 May 10 comment Paradox of the Relativistic Record Player yes, I see this has basically been answered in the link provided by @Lagerbaer. Is the correct protocol to now delete this question? May 8 comment Limit of Lorentzian is Dirac Delta thanks for the answer. So since the expression in question is NOT a form for the Delta function, it will be zero even if t=0. Is that right? May 8 comment Limit of Lorentzian is Dirac Delta thanks for the response. If I understand you correctly, you are also saying that the Lorentzian is a poor choice to define the Delta function by? Anyways, my test function is unity so I suppose I am fine considering 'my' definition to be ok for the Delta function. Mar 2 comment Kinematics textbook illustration @noname, What textbook is this? Feb 28 comment Can I calculate the height of a cliff from weight of falling object and time taken? @Frederik I think my y is your z Feb 26 comment Free falling of object with no air resistance I have always loved this deductive argument for equal velocities. The way I heard it is different but I think stronger. Assume one mass is very large and the other very small. If you tie them together with a massless rope or rod, you would expect the small mass to slow the large mass down if small masses fall slower. Hence, the two masses would fall somewhere in between the two velocities at which they would fall if they were separate. However, by looking at the system as a whole, the system of two masses should fall faster than heavy mass separately since the total mass is larger. Feb 19 comment On-site repulsion and Pauli exclusion Now, with what you've said (@Keenan), I must really wonder about the diagrams I'm seeing in these papers. They are showing one electron at an energy level εa. Then they show another electron hopping to that first electron's site. The new electron is placed at εa+U. With what you said, this seems to be incorrect b/c it suggests that there are two levels. Is there not a better way to draw this? Feb 19 comment On-site repulsion and Pauli exclusion Thanks Keenan. That is really insightful. It makes a lot of sense now that the overall energy is increases by U and not the energy of one electron (b/c which electron would it be anyway?). To follow up on one thing you said though, why would the two electrons necessarily be in a symmetric spatial state (which then of course leads to the singlet spin state)? Why not let them be in antisymmetric spatial state and then a triplet spin state? Feb 16 comment Energy levels in disordered organic semiconductors? Thanks. I think I figured out my problem. I thought I was reading that electrons existed in the LUMO states in the ground state equilibrium (which would no longer make it unoccupied). However the conditions were such that there is a voltage across the sample and charge is injected from an electrode (as you suggested was the case). This is what is putting electrons into the LUMO states and thereby making an overall non-zero net charge in the semiconductor.