Recent content by vela

One time, some punk made a comment about how grammar wasn't important because we understood what he meant. My English professor friend wholeheartedly agreed and added that it was best to avoid giving the impression to others that one is educated and literate. When I was in grad school, the...

One thought that occurs to me is that virtually all learning is self-learning. If you enroll in a course and listen to the lectures but don't do any of the work, you typically won't learn much at all. Most of what you do learn is acquired as you work through the material yourself. As I see it...

I'm pretty sure the OP means the surface in R3 defined by ##\theta = \pi/3## in spherical coordinates, which is a cone, and the sphere given by ##\rho = 4 \cos\theta##. The problem is to find the volume bounded by the cone on the bottom and the spherical cap on top.

Given the method, I think you should include the potential energy due to gravity (though you should've had ##-mgx##). It feels a bit arbitrary to omit it just because you might happen to know from a different analysis it effectively won't matter. It's straightforward to see it does indeed cancel...

Your teacher is not infallible, so I'd reach out for clarification about the intended function and intended domain. Note that your first series converges when ##\left\lvert \frac{z^2}2 \right\rvert < 1## or, equivalently, ##\lvert z \rvert < \sqrt 2##.

The problem statement explicitly says ##M## is heavy enough to cause the masses to slide up the incline.

The idea behind error propagation is to calculate the uncertainty in the result. Once you know the uncertainty, it tells you where to round to. The rules for sig figs are just general rules of thumb to estimate how the uncertainty propagates without having to do a proper analysis of error...

I think so too. There's some overlap, but there can still be a pretty big gap between the two majors. To properly prepare for physics grad school, I had to go back and earn a BS Physics.

Is PF a link-heavy site? In my brief look at a number of sites the other day, I noticed most sites don't underline every link, but they do for links in a block of text where the visual indicators help them stand out from the surrounding text. @Dale, does the underlining on a site like Ars...

Kagi search results, on the other hand, do have underlined links. So do the sites for the New York Times, the LA Times, the Washington Post, and the Wall Street Journal. That doesn't seem too surprising because newspapers probably prioritize making their sites accessible. I just checked a number...

Then I think it would help, as @robphy suggested above, if you could give us an example of a roadblock you're running into. Maybe you just need a quick review of a few chapters in Fundamentals of Physics II.

It is. My point was that if same spin meant both spin-up or both spin-down, it would correspond to only two of the triplet states and the solution wouldn't have admitted all three states and a threefold degeneracy.

The same thought occurred to me; however, the solution explicitly lists all three of the triplet states and claims there's a threefold degeneracy of the ground state. It's clearly admitting the possibility of the two electrons having opposite spin.

I don't get it either. I think he's wrong, but the same text is in the second edition. I would think that an obvious error like that would have been caught and corrected already, so perhaps we're both missing something here. I had the same thoughts reading through his solution. It seems he...

Isn't the complex logarithm traditionally denoted ##\log##, not ##\ln##? I noticed in a couple of places you used principle where you meant principal.