mathemathical physics Definition and 9 Threads

I would love to hear from you if you have any suggestions, feedback, or criticism. The goal is to build better and more sophisticated software that would push the boundaries of research in astrophysics!

By looking around, it seems like Dr. Hassani's books are great for studying "mathematical methods for the physicist/engineer." One is for the beginner physicist [Mathematical Methods: For Students of Physics and Related Fields] and the other is [Mathematical Physics: A Modern Introduction to Its...

I’ve attached my attempt. I’ve tried to use triangle inequality formula to attempt, but it seems I got the value which is larger than 1. Which step am I wrong? Also, it seems I cannot neglect the minus sign in front of e^(N+1/2)*2pi. How can I deal with that?

Here’s my work: The integrating factor I find is (x^(2)-1)^1/2. The self adjoint form I find is -d/dx (((1-x^(2))^(3/2))*dy/dx))=k(x^(2)-1)^(1/2). Am I right?

Is there a Kroneker Delta identity: $$ \delta^3 (k) \delta^3 (k) = \frac{2\pi^2}{k^3} ~ \delta (k_1- k_2) $$? Where k is a wave number. In this Paper: Equations 26 and 27, I think this identity is used to make ##k_1=k_2## and there is an extra negative sign.

The trace of the sigma should be the same in both new and old basis. But I get a different one. Really appreciate for the help. I’ll put the screen shot in the comment part

I have read some text about defining the cross product. It can be defined by both a x b = epsilon_(ijk) a^j b^k e-hat^i and a x b = epsilon^(ijk) a_i b_j e-hat^k why the a and b have opposite indice positions with the epsilon? How to understand that physically?

HI, I am an International Student studying in the US (at a "liberal arts" small college ranked in the Top 20 as per US News Rankings). I will graduate in 2024 and intend to apply for PhD programs in Mathematical Physics starting October 2023 for admission in 2024. GPA: I am a double major in...