Recent content by cstalg

I think the temperature of the detector should be as low as possible, so that no thermal noise will disturb the observation. So it's T'=0. Is that right?

Homework Statement Problem 2.11 of Liboff's Introductory Quantum Mechanics, 1st edition Suppose that you are inside a blackbody radiation cavity which is at temperature T. Your job is to measure the energy in the radiation field in the frequency interval 10^{14} to 89 \times 10^{14}...

Yes, such properties are "suggested" by Noether's theorem. So the form of Lagrangian is defined, not proved. Also we need not define "any (physically meaningful) quantity" have such properties. All the other conservation laws are corollaries of certain symmetries of Lagrangian.

Thank you, lugita15. But this is just the same as what Landau said, without more sophisticated details. We know that if L(\mathbf x+\delta \mathbf x, \mathbf v, t)-L(\mathbf x, \mathbf v, t)=df(\mathbf x,t)/dt, then we get the same equation of motion. So generally, the Lagrangian could be a...

As we know, the variational principle can be used as the fundamental principle of mechanics. Without knowing Newton's laws, the Lagrangian could be derived from symmetric consideration. As the simplest case, the Lagrangian of a free particle could be derived from Galileian invariance, or the...