# Recent content by LuccaP4

1. ### Solid-state Physics: Fermi surface and necks in an FCC structure

Does anyone have some bibliography about necks in FCC structure Fermi surface? I have to solve this problem and I have no idea how to start. Thanks.
2. ### I 4th-rank isotropic tensor

I have this statement: Find the most general form of the fourth rank isotropic tensor. In order to do so: - Perform rotations in ## \pi ## around any of the axes. Note that to maintain isotropy conditions some elements must necessarily be null. - Using rotations in ## \pi / 2 ## analyze the...
3. ### Hamiltonian mechanics: phase diagram

Okay, then I'll do that. Thanks.
4. ### Hamiltonian mechanics: phase diagram

But the statement says to write it in spherical and cylindrical coordinates. I have to build the phase space in that coordinates.
5. ### Hamiltonian mechanics: phase diagram

The issue here is that I don't know how to operate the final equations in order to get the phase diagram. I suppose some things are held constant so I can get a known curve such as an ellipse. I attach the solved part, I don't know how to go on.
6. ### Lagrangian mechanics: central-force-like problem

Okay, thanks!
7. ### Lagrangian mechanics: central-force-like problem

Is this valid in every case? In the frecuency ##\omega##, I should evaluate the second derivative in ##r_0##, shouldn't I?

Many thanks!
9. ### Given the following graph, answer the following questions: increasing, decreasing, or constant?

I'm not really sure, but if in ##x=-6## there is an asymptote, then the function is not defined in ##\left(-\infty,-6\right]##
10. ### Need help deducing the region for this double integration problem

You can use inequalities in geogebra as well.
11. ### Given ##f(x)=3x^5-5x^3##, find all critical points.

I think it's fine, but I agree with @haruspex that you have to check the factorisation of ##y''##. Just a friendly reminder: there are critical points as well where the derivative doesn't exist. In this case, the first derivative exists for every ##x##, so you don't have to matter.
12. ### Question about the solution of this system of equations

As @Mark44 says, its the same expression. An integer ##k## could be positive or negative, so if you take ##2k## or ##-2k##, both determines the same set of integers, which is positive and negative even integers. ##k=\left\lbrace...,-3,-2,-1,0,1,2,3,...\right\rbrace ##...
13. ### Curve sketching (discussion)

Be careful! There are 2 types of critical values. First type are the ones that makes ##f'(x)=0## or where the first derivative doesn't exist. Second type are the ones that makes ##f''(x)=0## or where the second derivative doesn't exist. First type critical values could be extremes (maximum or...
14. ### Given the following graph, state the intervals concave down

I think is correct. The second derivative in ##x>0## equals ##0## and in ##-6<x<-2## the function is concave up. ## x=-2 ## would be the point of inflection.
15. ### Lagrangian mechanics: central-force-like problem

I copy again the statement here: So, I think I solved parts a to c but I don't get part d. I couldn't even start it because I don't understand how to set the problem. I think it refers to some kind of motion like this one in the picture, so I'll have a maximum and a minimum r, and I can get...