The electron in a hydrogen atom occupies the combined spin and position state

(a) If you measured the orbital angular momentum squared (L²), what values might you get, and what is the probability of each?
(b) Same for the z component of orbital angular momentum (L_z).
(c) Same for the spin angular momentum squared (S²).
(d) Same for the z component of spin angular momentum (S_z).
Let J Ξ L + S be the total angular momentum.
(e) If you measured J², what values might you get, and what is the probability of each?
(f) Same for J_z.
(g) If you measured the position of the particle, what is the probability density for finding it at r,θ,Φ?
(h) If you measured both the z component of the spin and the distance from the origin (note that these are compatible observables), what is the probability per unit r for finding the particle with spin up and at radius r?

Transcribed Image Text:

(√1/3YX+ + √2/3Y| x-).