Recent content by vela

No, he's saying taking ##\hbar=m=1## is effectively the same as what I explained above about using the natural length scale for the harmonic oscillator, though I think you also need ##\omega = 1##. Your (dimensionless) ##x## is the same as my ##u## but different than the ##x## in the expression...

Zettili is unfortunately using ##\hat X## and ##\hat P## to represent both the regular position and momentum operators in some contexts and the dimensionless position and momentum operators in others, which is what's causing your confusion. The natural length scale for the harmonic oscillator...

You might get the answer you're looking for, but that's by coincidence. It's not the correct way to solve your problem.

How are ##\beta## and ##k## defined? What are the conditions that must be met at ##x=W/2##?

If your goal is to learn physics, you might want to hold off on focusing too much on the theorems and proofs at this stage and concentrate instead on being able to do calculations and developing intuition. Halliday and Resnick is an introductory physics text, suitable for students who are...

Oh, you were asking about the steps preceding that last step. Yeah, the OP isn't exactly forthcoming with his reasoning.

##F = -kr## implies ##\omega = \sqrt{k/m}##.

What precisely is stopping you from writing down an expression for ##U(r)##?

No. If you're treating ##y## as a constant, its derivative with respect to ##x## is 0.

I'm inclined to agree with your reasoning and answer.

I think you're suffering from the problem every physics student seems to go through when first encountering quantum mechanics: you're trying to make sense of the theory in terms of everyday, classical ideas. That's a fool's errand since you're supposed to make sense of classical mechanics in...

I know you already solved the problem, but I thought I'd point out the reasons why what you tried didn't work. The equation you are referring to doesn't apply to the given circuit. It only applies to the basic RC circuit—a battery, a resistor R, and a capacitor C connected in series. That's...

For example, I would interpret "##P(V_x)## and ##V_x## are ##P/V##" to mean ##P(V_x)=V_x=P/V##, which doesn't make sense.

I don't understand what this means.

While you can certainly do that, why would you want to?