I managed to solve a few things but the remaining problem is about degeneracy :
for I1 = I2 = 1/2
I=I1+I2
what are the degeneracies for I² ?
for I we have (2I1+1)*(2I2+1) = 2*2 = 4
but for I² is it just d(I) * d(I) = 16 ?
Homework Statement
S=1/2
I1=I2=1/2 (nuclear spin)
I=I1+I2
J=S+I
Homework Equations
H= a S . I1 + a S.I2
The Attempt at a Solution
A) Find the values of I, the eigenvalues of I2, their degree of degeneracy and show that [H,I2]=0Using momentum addition I get
I = 0 or 1
I2 has for...
Homework Statement
Finding eigenvalues of an hamiltonian
Homework EquationsH = a S²z + b Sz
(hbar = 1)
what are the eigenvalues of H in |S,M> = |1,1>,|1,0>,|1,-1>
The Attempt at a SolutionH|1,1> = (a + b) |1,1>
H|1,0> = 0
H |1,-1> = (a-b) |1,-1>
which gives directly the energy :
a+b , 0 ...
I have been a little busy, I'm sorry for not answering sooner.
It should be on this form then :
| eigenvalue of S2 , eigenvalue of Sz >
##\frac{C}{3}## for |2,1>
##\frac{C}{3}## for |2,-1>
##\frac{-2C}{3}## for|2,0>
And if we add a magnetic field B oriented on the z axis (in interaction...
I haven't studied much the eigenvalues of the spin but I can try. (I am not sure at all) :
Sz = +1/2 , -1/2
S=1
Then H0=C(1/4-1/3) = -C/12
eigenvalues K=-C/12
and I should look for something who satisfy :
H0Ψ=KΨ
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