- #1
Dario SLC
Hello, I have a doubt about the Complete Set of commuting observables (CSCO) in the cases when there are a magnetic field ##B## in z.
The statement is find the constant of motion and CSCO for a particle of mass m and spin 1/2, not necessary a electron or any atomic particle.
I know that the CSCO is ##\{\hat{H}, \hat{L^2},\hat{L_z},\hat{S_z},\hat{S^2}\}## if not active the magnetic field, and them are constants of motion.
If not consider the coupling ##\hat{L}\hat{S}##, I think that the CSCO do not change, ie, conserve the constants of motion. But if I consider ##L\cdot S##, the new CSCO is ##\{\hat{H}, \hat{L^2},\hat{J_z},\hat{J^2},\hat{S^2}\}## (in absent of field ##B##)
That is true?
(The potential ##V##, is a spherical potential, only depends of ##r## coordinate.)
The statement is find the constant of motion and CSCO for a particle of mass m and spin 1/2, not necessary a electron or any atomic particle.
I know that the CSCO is ##\{\hat{H}, \hat{L^2},\hat{L_z},\hat{S_z},\hat{S^2}\}## if not active the magnetic field, and them are constants of motion.
If not consider the coupling ##\hat{L}\hat{S}##, I think that the CSCO do not change, ie, conserve the constants of motion. But if I consider ##L\cdot S##, the new CSCO is ##\{\hat{H}, \hat{L^2},\hat{J_z},\hat{J^2},\hat{S^2}\}## (in absent of field ##B##)
That is true?
(The potential ##V##, is a spherical potential, only depends of ##r## coordinate.)