#10 I need the answer in detailed steps ans explanations A particle of spin 1 an
ID: 1060275 • Letter: #
Question
#10 I need the answer in detailed steps ans explanations
A particle of spin 1 and a particle of spin 2 are at rest in a configuration such that the total spin is 3, and its z-component is 1 (that is, the eigenvalue of S_z is h). If you measured the z-component of the angular momentum of the spin-2 particle, what values might you get, and what is the probability of each one? An electron with spin down is in the state psi_510 of the hydrogen atom. If you could measure the total angular momentum squared of the electron alone (not including the proton spin), what values might you get, and what is the probability of each?Explanation / Answer
a) We use the Clebsch Gordan coeffcients to write the total state of the system
| 3,1) = C1,2,3m1,m2,1 |1,m1) |1,m2) for all m1+m2 =1
non-zero Clebsch-Gordan coeffcients are found from tables
C-1,2,11,2,3 = ; C 1,0,11,2,3 = ; C0,1,11,2,3 =
Just take the square of the amplitude
So, that you would get values of probabilities
b) The electron spin states | 1,0) is (1/2 , -1/2)
Again use the Clebsch Gordan coeffcients for the electronic spin state
to get possible values of s
| 1,0) (1/2 , -1/2) = C0,-1/2,-1/21,1/2,s |s-1/2)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.