Recent content by Physicsdudee

Thanks for the help. I have read into the article already some time ago. I am noticing that I have misunderstood the assignment given, I think, at least the way I understand the assignment now makes more sense. I will give it a go.

Yeah, well I was thinking the same thing, that is why I was confused about it, the question itself seemed a bit unclear.

I need to prove one aspect of the given definition, namely the aspect that <Af,Ag>=<f,g>

Well, my definiton of a unitary operator is the following: Let A be a unitary operator, then A is bijective and <Af,Ag>=<f,g> where f,g is an element of L2.

Hello folks, I need to show that a unitary operator obeys <Af,Ag>=<f,g>, where A is a unitary operator. However, I am technically not yet given the fact, that the adjoint of A is equal to its inverse, and that is the problem. I have no clue how to prove the given task without using the...

Haha that’s so kind, I appreciate it:)

Yep, I know Geo gebra but I was so eager to actually not use anything because in the exam it’s not going to be any different. But I get your point, making use of all these nice tools is extremely good for visualizing

Yes, that seems easier, thanks a lot!

Thanks for your reply. If I were to use cylindrical coordinates, then I assume I would let φ range from 0 to 2π, z from -1 to 1. But what about R then? R should be a function of the height regarding integration over the cone and then another function of height regarding integration over the...

Okay so I know, that if the radius is 0, the z coordinate will run from -1 to +1. If the radius tends to one, the z coordinate will tend to 0. But I still cannot imagine how this set looks like, help would be appreciated. Thank you.

Thank you for the hint, I had totally forgotten about that trick. I think that made it work:)

Hmm yeah that makes sense. Tbh I don't really get the question we were given either. It said that we must calculate escape velocity using the Lagrange equation, that's it. But yeah, I will try to find a way, maybe some idea pops up.

Hmm I mean I know that r and v are related in a way that dr/dt=v and vice versa with the integral. I could replace the v' in this differential equation you posted with r''. That would give me a second order differential equation in terms of r, however, if I solve for r, I get a function r(t)...