Physics, 24.04.2020 22:31, macymichtavy
Noether's theorem asserts a connection between invariance principles and conservation laws. In Section 7.8 we saw that translational invariance of the Lagrangian implies conservation of total linear momentum. Here you will prove that rotational invariance of ,C implies conservation of total angular momentum. Suppose that the Lagrangian of an N-particle system is unchanged by rotations about a certain symmetry axis.
(a) Without loss of generality, take this axis to be the z axis, and show that the Lagrangian is unchanged when all of the particles are simultaneously moved from (rα, θα, ϕα) to(rα, θα, ϕα + ϵ) (same ϵ for all particles). Hence show that ∑ N α = 1 ∂ L ∂ ϕ α = 0 ∑α=1N∂L∂ϕα=0
(b) Use Lagrange's equations to show that this implies that the total angular momentum Lz about the symmetry axis is constant. In particular, if the Lagrangian is invariant under rotations about all axes, then all components of L are conserved.
Answers: 1
Physics, 22.06.2019 11:00, velazquezemmy45
What would be the result of an alpha particle coming into a magnetic field? a) the alpha particle will stop moving. b) the alpha particle will reverse its direction. c) the alpha particle will be deflected in a curve path. d) the alpha particle will continue to travel in a straight line.
Answers: 1
Physics, 22.06.2019 12:30, cardsqueen
Consider a hydrogen atom in the ground state. what is the energy of its electron? =e= jj now consider an excited‑state hydrogen atom. what is the energy of the electron in the =5n=5 level? =e5= j
Answers: 3
Noether's theorem asserts a connection between invariance principles and conservation laws. In Secti...
Mathematics, 13.06.2020 18:57
Mathematics, 13.06.2020 18:57
Mathematics, 13.06.2020 18:57
Mathematics, 13.06.2020 18:57