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.(adsbygoogle = window.adsbygoogle || []).push({});

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.)

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# Homework Help: Quantum constant of motion in a magnetic field

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