1 20 Points The Electron In A Hydrogen Atom Is In The State Rs Erix V X X R32 A 5 Points The 1 (26.46 KiB) Viewed 49 times
1 20 Points The Electron In A Hydrogen Atom Is In The State Rs Erix V X X R32 A 5 Points The 2 (29.78 KiB) Viewed 49 times
(1) (20 points) The electron in a hydrogen atom is in the state * = Rs (√erix + √=v²x + √=√³x) R32 +) (a) (5 points) The total angular momentum is the sum of 5 and L. What are the possible values of the square of this total angular momentum, and what is the probability of each? (b) (5 points) What possible results could a single measurement of the projection of this total angular yield, and what is the probability of each? (c) (5 points) What is the probability for finding the electron near a position (r,0,0). (d) (5 points) What is the probability to find a particle in the spin up state and near the position (r, 0, 0).
(2) (20 points) Consider the case of two angular momenta, j₁ = 1 and j2 = . (2.1) (10 points) Using the table of Clebsch-Gordon coefficients on page 188 in Griffiths, write out all the coupled states in terms of uncoupled basis functions. (2.2) (10 points) Start with the resultant state with the highest value of j and m, and apply the lowering operator j=j+j2 twice in succession and show that you get two of the states from (2.1). Pay attention to the normalization at each step. (3) (10 points) Quarks are spin 1/2 particles and the proton (and neutron) on average contain 3 quarks. What are the possible values of the total spin angular momentum of the proton (and neutron)? Which of these values is observed experimentally?
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