Recent content by HubertP

This makes sense now! To make sure it's consistent I tried expanding this \Delta A in eigenbasis of A, using A = \sum\limits_n a_n \left|a_n\right\rangle \left\langle a_n\right|, and applying it to a ket vector - I got correct result (sum of squared deviations of eigenvalues from mean...

I'm trying to get my head around quantum mechanics with the help of Sakurai "Modern Quantum Physics". It's been good so far, but I came across a formula I don't really understand. When discussing uncertainty relation (in 1.4) the author begins with defining an "operator": \Delta A \equiv A -...

That's what I thought, more or less. So it's only the real symmetries with respect to Lagrangian that can be associated with conserved quantities. Unfortunately I don't know much about Lagrangian formulation of relativistic field theory. Hope to know more before I die :) Anyway, I know what...

Looks like I need to resurrect the thread that seemed to be closed! In my first post I asked whether demanding that Lagrangian does not change under transformation that is expected to leave laws of physics unchanged is correct way of thinking. The reason for my question was that there is...

This really starts to make some sense to me. Thank you! I greatly appreciate your help and time you spent on it. Indeed, I not only added potential (which could possibly be identified with some fictitious force acting on the system due to non-inertial frame), but also modified the kinetic term...

Yes, exactly. I was just surprised to see that there can be Lagrangians which depend explicitly on position or time, which still yield the same equations of motions after translation - like the one in my example. Now I wonder if it's because they describe the isolated systems (and thus...

I fully agree with your example. The Lagrangian is valid, it describes isolated system (no explicit time dependence - potential only depends on distance between system components and not the absolute positions). In such case it's obvious that translation will not change the Lagrangian. Your...

Thanks for your answer, K^2! Now that I'm looking at my post again I realize I didn't formulate it properly. Speaking about time derivative of function F, which, when added to Langrangian, does not change the equations of motion, I should have written F(q,t) instead of F(q,\dot{q}) In...

This is my first post, so hello everybody. I don't have university background and english is not my native language, so please forgive me if what I'm writing is hard to understand sometimes. I'll do my best to be clear. I've always loved physics in general, but recently came to conclusion that...