Recent content by whatisreality

This isn't explained anywhere so it must be super basic and I'll probably kick myself for not getting it, but on the wiki page for time independent perturbation theory, section 3.1: https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics) It talks about first order corrections and...

Homework Statement I've never encountered Jacobians before, and having read up on them a bit I find the wording of the last part of this question confusing: A set of coordinates ##x'_{\mu}## in frame B is obtained from the set ##x_{\mu}## in frame A, by boosting B w.r.t A with speed beta along...

Homework Statement In a computational basis, a qubit has density matrix ## \rho = \left( \begin{array}{ccc} \frac{1}{2} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{2} \\ \end{array} \right)## At t=0. Find the time dependence of ##\rho## when the Hamiltonian is given by ##AI+BY##, ##A## and ##B##...

I've been reading these notes: http://www.vcpc.univie.ac.at/~ian/hotlist/qc/talks/bloch-sphere-rotations.pdf And on slide 11, to check what the rotation operator is doing, the state is pre- and post-multiplied by the operator so that the calculation performed is ##\rho' = R\rho R^{\dagger}## Why...

Thanks for your help, spotted my mistake, I just rearranged wrong. My last two lines don't follow from each other. Silly mistake!

Yes, that's wrong too, I saw ##I_m## and ##V_m## in my notes and assumed they meant maximum current and voltage rather than current and voltage at max power, I should have thought that through.

1. The problem statement, all variables and given/known da Show that for a PV cell finding a maximum of power leads to the following equation: ##(1 +\frac{qV_{max}}{kT})\exp\left(\frac{qV_{max}}{kT}\right) = 1 + \frac{I_{sc}}{I_{rs}}## ##I_{sc}## is short circuit current and ##I_{rs}## is...

Would you say then that ##k## is the class width of the single histogram bar being considered? That's how I've interpreted it. I also thought it would be quite a strange coincidence if the number of events ##n## recorded, which corresponds to the area of the bar, happened to be also the average...

Homework Statement If one bar of a histogram has been generated with ##n## entries from a total of ##x## measurements, i.e. the event occurs randomly ##n## times in the ##x## event interval, then what is the standard deviation of values in this bar? Let ##k## be the range of values that could...

Homework Statement Using conservation of energy, show that the 4-velocity ##u^{\mu}## of dust satisfies: ##u^{\mu}\nabla_{\mu}u^{\nu} = f u^{\nu}## Explicitly identify ##f##, which is some function of ##u^{\mu}##, ##\rho## and their derivatives. And show that this equation becomes...

But in the line directly beneath that box, it looks to me like the christoffel symbol got moved inside the partial derivative. That might not actually be what's happening, I'm not sure of that step.

I have a couple of questions about how Christoffel symbols work. Why can they just be moved inside the partial derivative, as shown just beneath the first blue box here: https://einsteinrelativelyeasy.com/index.php/general-relativity/61-the-riemann-curvature-tensor And if you had the partial...

When I say how does the contraction work, that makes it sound worse than it is, I think. I do know what a contraction is, what I wanted to double check is that I can relabel a contravariant index to be the same as the covariant. I'll definitely go back and re-read my notes though, it's always...

Homework Statement I've been given the Bianchi identity in the form ##\nabla _{\kappa} R^{\mu}_{\nu\rho\sigma} + \nabla _{\rho} R^{\mu}_{\nu\sigma \kappa} + \nabla _{\sigma} R^{\mu}_{\nu\kappa\rho} =0##Homework EquationsThe Attempt at a Solution In order to get from this to the Einstein...

Ok I think I understand. Definitely not as simple as just scrubbing any two symbols that are the same! I'll take a look at what the actual mathematical operation is. Thank you for your help and for such detailed answers, I really appreciate it!