Problem

The electron in a hydrogen atom occupies the combined spin and position state(a) If you me...

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 (Lz).


(c) Same for the spin angular momentum squared (S2).


(d) Same for the z component of spin angular momentum (Sz)

Let J ≡ 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 Jz.


(g) If you measured the position of the particle, what is the probability density for finding it at r, θ, ф?


(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 density for finding the particle with spin up and at radius r?

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