Recent content by vela

You're assuming the usual momentum operator is valid for a particle confined to a finite region.

Is synchronization that important? For each course here, we have a course outline of record (COR), which lists the topics that should be covered. Other schools can refer to the COR to determine whether it's willing to accept the course for transfer. The department faculty decide what topics...

Here, we don't see a surcharge for using a credit card for most bills. Typically, you only see a surcharge when dealing with the government, like paying the DMV or paying property taxes. You can avoid those fees by having the payment deducted electronically from a checking or saving account...

For the vast majority of people in the US, I'd say the need to write a check is much more common than the need to milk a cow. On the one hand, I've had to write about 25–30 checks over the past fourteen years. It's rare that I need to, but it's still way more than I expected to when I opened my...

You can go old school and look it up in a dictionary. According to the American Heritage Dictionary, the definition of right is "Of, belonging to, located on, or being the side of the body to the south when the subject is facing east." This is what I got when I searched for "what are the...

While increasingly rare, there are still situations where they still need to know how to write a check. Analogue clocks are still pretty common, so being able to read one is still useful. I like to tease my astro students and jokingly ask if they can read the clock in the classroom. Maybe I...

Given that the top branch is identical to the bottom branch, the fact that you concluded the current somehow flowed in opposite directions in the two branches should have made you realize you made a mistake somewhere in your nodal analysis. Or to put it another way, using the symmetry, you...

Griffiths went through the same derivation for ##\nabla \cdot \frac{\hat r}{r^2}## to show that there's a delta function at the origin. You can use this result without going through the derivation each time. Griffiths expressed the electric field in terms of ##\nabla \cdot \frac{\hat r}{r^2}##...

I use it mainly for the same reason @weirdoguy stated. It's a pain to keep writing the square root down, and not using it makes the equations look unnecessarily complicated. Another reason is that I find my students are notoriously bad at calculating things. If they can calculate ##\gamma## just...

You need to learn how to learn. For each person, it's different, so asking exactly what steps you have to take is misguided. Assess if what you're doing is actually working. If it's not, try something different. Quit obsessing over grades. You want primarily to focus on learning, not getting an...

Using Mathematica, I expanded ##j_1(x) - \tfrac{x^2}{10}(j_1(x)+j_3(x))## in a series and plotted the result keeping only the first three non-vanishing terms. This is what I got. The function never crosses the axis for ##x>0##, so I'm surprised you found ##x \approx 0.79##. So one mistake seems...

Can you point out specific instances where you think he doesn't understand physics? In what little I've seen of him discussing topics in physics, I don't recall any instances where I thought he was wrong. To be fair, I'd say that's true of almost everyone I've heard discussing trans issues. I...

You have $$a = v \frac{dv}{dx}$$ where ##x## is the displacement. As the block initially moves to the right, you have ##x=s##, so the equation you derived works. When the block moves to the left, however, you no longer can say ##x=s##, but you can say that ##dx = -ds## which gives you the minus...

I assume you're troubled by the fact that when ##\alpha > \pi##, the expression you derived gives you ##v^2<0##. When ##\alpha = \pi##, what's the velocity of the bar and which way does the force point?

Consider which way the velocity of the hour hand's tip points at that moment.