3) The electron in the |3,1,1> state of a Hydrogen atom is replaced with a spin-1 particle X. (For simplicity, just assume identical charge and mass as an electron.) The new particle is still in the 13,1,-1> state (in |n,l,m> notation). The z-component of the spin angular momentum of X is measured to be ħ. A "J." and a " J?" measurement are then made on X. (Measuring the combined angular momentum magnitude, orbital + spin.) What are the possible results, and what are the probabilities of each result? (Give measurement results, not quantum numbers.) (Use The Clebsch Gordon Table 11.5, which shows how to add l=1 and s=1 angular momenta.)
3) The electron in the |3,1,1> state of a Hydrogen atom is replaced with a spin-1 particle X. (For simplicity, just assume identical charge and mass as an electron.) The new particle is still in the 13,1,-1> state (in |n,l,m> notation). The z-component of the spin angular momentum of X is measured to be ħ. A "J." and a " J?" measurement are then made on X. (Measuring the combined angular momentum magnitude, orbital + spin.) What are the possible results, and what are the probabilities of each result? (Give measurement results, not quantum numbers.) (Use The Clebsch Gordon Table 11.5, which shows how to add l=1 and s=1 angular momenta.)
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