Recent content by leinadle

I suppose the answer to my question must be no, after reading your response again. If I consider the set S which consists of all positive reals then each element is individually bounded by the x+1 argument, but S is certainly not bounded since R is unbounded. However, this logic is really...

Sorry for the vagueness, here is an example. Suppose we have an infinite sequence of functions {f_n(x):R -> R}, each of which is bounded by some M_n > 0; i.e. |f_n(x)| < M_n for all x in R. Can we say that there exists an M > 0 such that |f_n(x)| < M for all n and for all x in R?

This is a concise question, so the title pretty much says it all. Also, this is not a HW question, but the idea has subtly popped up in two homework problems that I have done in the past. I cannot justify why the entire set would be bounded, because we know nothing of the nature of the...

So what makes the rounded square well a better approximation? Why is it sensible to have the potential start to vary near the edges rather than stay zero?

On an introductory level, yes. Are you saying the potential energy profile is solely due to the superposition of electric fields from surrounding charges? I guess my confusion with that is the sudden jumps that I'm seeing in the potential energy for finite square wells and the tunneling...

Hi all, I'm having conceptual troubles understanding the significance of the potential energy term in Schrodinger's equation. More specifically, the physical meaning of the potential "wells" is not clicking with me; my textbook is not making this very clear. For clarity, consider an...

A useful analogy for understanding why a resistor impedes current is the following: Imagine you have balls rolling down a smooth hill (potential difference), and they will roll down this hill as quick as possible if there is nothing in the way. However, imagine now that the hill is covered in...

Ah, I see. Thanks for the quick response!

The explanation for this is probably very trivial, but I am not seeing it. I'm reading through Ramamurti's "Basic Training in Mathematics" and in the Multivariable Calculus section for spherical coordinates he says and then shows an integral. Shouldn't there be a negative sign before the cosθ...

Mathematically, as mfb said, the summation of a sine and cosine is the solution to the differential equation that governs simple harmonic motion. For a mechanical oscillator, this equation is mx''+kx = 0, and the general solution is x(t) = c1*cos(wt+p)+c2*sin(wt+p). If you want a more intuitive...

Great post in that other thread, I didn't see that! OP should definitely go over there.

I am reading through The Feynman Lectures and chapter 4 of the first volume is on conservation of energy, and I think his section on "what is energy?" is terrific. Here are a couple paragraphs from that section:

Danger's post #13 is a great description. Understand sound by what it is mechanically: a bunch of atoms slamming into their buddies.

What is the source of your data?

How comfortable are you with vector calculus? You can visualize Lagrange Multipliers by realizing the constraint is a curve on your surface, and finding where the gradient vectors are parallel to each other finds either the minimum or maximum of your system of equations. Here is a good...