Recent content by randomafk

I'm looking through Nielson's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how to do this, or how to verify it (fig 4.8 in his book) I've attached a photo of the diagram...

Hmm, okay. So then, just like in a single particle system, if I measure the system then I have a 1/2 probability of collapsing the wave function into one of those two possible configurations? I'm not quite sure what you mean that the labels don't matter. I thought the problem lies in the fact...

When dealing with n-particle systems that are identical, is the superposition of them just a mathematical construct, or is it similar to how the state of a single particle can be in multiple eigenstates until its measured. For instance, if I have two fermions: \Psi = \Psi_a(x_1)\Psi_b(x_2) -...

So, when dealing with the Hydrogen molecule (H2) we know each electron is antisymmetric since they're fermions i.e. \Psi_\_ = 1/\sqrt(2) * (\Psi_a(r1) * \Psi_b(r2) - \Psi_b(r1) * \Psi_a(r2)) and then similarly for the spinor such that the total state, \Psi\chi is antisymmetric When you deal...

Like the title says, why are the only possible values of an operator its eigenvalues? reading shankar right now and I'm having difficulty understanding why this has to be the case, given some operator/variable Ω

Oops. Sorry for the vague language, but when I said distinct eigenvalues I did indeed mean multiplicity of 1! But anyway, where does that fact follow from? My understanding of the proof that eigenvectors of distinct eigenvalues are independent is something like this (in the special case of n...

Hey guys, I've been trying to brush up on my linear algebra and ran into this bit of confusion. I just went through a proof that an operator with distinct eigenvalues forms a basis of linearly independent eigenvectors. But the proof relied on a one to one mapping of eigenvalues to...

I'm currently learning about different types of compressional work. The book I'm using covers mostly just isothermal and adiabatic processes, which make sense. Isothermal being so slow that everything equilibriates while adiabatic is so fast that heat cannot escape. However, the book briefly...

Hi all, I'm trying to understand exactly what the physical meaning of conductivity/current is in relation to waves. if we have a wave traveling through a conductor, we find that it decays exponentially, i.e. e^{-\alpha z} where \alpha=imag(k)=\omega\sqrt{\frac{\epsilon\mu}{2}}...

Ah. Thank you. That definitely helps a lot. The solution from the manual is: "If free to rotate, it would start out in the 'diamond' orientation, switch to 'square' for the middle position, and then switch back to diamond, always trying to present the minimum chord at the field's edge" I'm...

Shouldn't the nonvertical forces cancel out in both the diagonal and square cases though? And here is the problem, verbatim. 7.46) Refer to Prob 7.11 (a) Does the square ring fall faster in the orientation shown (Fig 7.19 [attached]), or when rotated 45° about an axis coming out of the page...

Oh, okay. Yes, that makes sense. I feel sort of silly now. The backemf is generated differentially so it's just a simple differential equation to solve for it.. Thanks!

Thanks for the clarification. So the back emf and IR must add up to the applied emf. My confusion/question still remains though. That is, if we apply a back emf don't we change the rate at which current changes over time (if it has a nonzero second derivative)? If so, wouldn't this induce...

Apologies, for that, I did not copy the question verbatim. B points into the page and occupies the top portion of the loop. However, this is similar to your situation where it points out of the page but takes up the bottom portion. The question is a bit vague when it says it's allowed to...

Hi, I have a question about back emf So, my understanding of back emf (\epsilon_b=-L\frac{dI}{dt})is that its the counter voltage that's induced by change in current, whether it be from a battery or magnetic field (\epsilon_0). We can model this as an LR circuit where \epsilon_0 +\epsilon_b=IR...