Recent content by SgrA*

Hello, I wanted to study the behaviour of electrons in a spatially bounded system. I want to have a larger number of electrons, but I took 3 to start with and arrived at this system of coupled equations: \begin{align}\begin{bmatrix} \mathbf{\ddot{x_{1}}}\\ \\ \mathbf{\ddot{x_{2}}}\\ \\...

I mean, I got it right, but I'm not confident that I can get math right, yet. Hopefully more problems and I'll feel confident about my solutions. Thanks for asking! :)

Thanks for verifying, I'm still not very confident. :)

I've recently started reading Shankar's book. I'm still in the first chapter, where he first prepares you for the math. On the basis of the first chapter, I'd highly recommend that book: clear explanations, adequate (but not excessive) examples, and in text exercises with gradually increasing...

Hello, Here's a textbook question and my solution, please check if it is correct, I'm slightly doubtful about the second part. Consider Hermitian matrices M_1, M_2, M_3,\ and\ M_4 that obey: M_i M_j+M_j M_i = 2 \delta_{ij} I \hspace{10mm} for\ i,\ j\ = 1,\ ... ,4 (1) Show that the eigenvalues...

This is not exactly a homework question. In a physics textbook, they derive an expression for gravitational redshift of a photon emitted by a star at a large distance from the source by taking photon as a mass traveling up, against a gravitational potential and hence expending its...

Hi, What is the molecular-level mechanism of shear-thickening of oobleck (cornstarch-water paste)?

Hi, Thanks for the reply and sorry, took me long to follow up. I have been trying it, and in the equations, the mass of the ball would directly be the mass on the spring, correct? What would the spring constant be? I know it has something to do with the curvature of the surface, but I'm not...

Hi, I'm considering this set up: A vessel with a curved (parabolic?) inner surface is rotating at an angular speed ω. Two heavy balls are placed near the axis of rotation of the vessel. Due to centrifugal force, the balls move outwards towards the edge. This increases the moment of...

Oh, alright. Thanks, everyone!

I wanted to evaluate it analytically, but apparently that's not possible. I'd like to know what tells you that, though, so I don't waste time again, trying to evaluate integrals like the one mentioned above.

I understand that, but why is it so? Rather, how can you tell that there is no point in trying to evaluate it?

I think I'm on the totally wrong way then. I'm trying to get familiar with Lagrangian mechanics, so after figuring out the basics, I wanted to try numerically verifying that it is consistent with Newton's first law. I considered a particle moving with a constant velocity v, which has an...

I wanted to integrate kinetic energy \frac{1}{2}mv^{2} with respect to time dt. v would be \frac{dx}{dt}, but I'm not sure how I'd do it.

How do I perform this integration: \int \left (\frac{dy}{dx}\right)^{2} dx Thanks!