What Are the Possible Values of Lz for an Electron in This State?

[dg88]

Hi,

I just came across a question that goes like this:

Consider an electron in a state |l=3, s=1/2, j=5/2,mj=3/2>

1) Find the possible values of Lz in this state.

2) Find the expectation value of Lz in this state.

It would be great if some one could guide with this question.

Thanks

 

[malawi_glenn]

we never give full solutions..

however, I can give you a hint:

expand |l=3, s=1/2, j=5/2,mj=3/2> in the basis of |l,m_l> and |s,m_s>

using a clebsh gordan table

if l = 3 and s = 1/2 and m_j = 3/2, then you can find out what m_l and m_s is contributing to this state since m_j = m_s + m_l (scalar addition)

 

[dg88]

thanks lot for your help...Actally I am having some trouble unerstanding this whole conceptI will tr it out.

 

[malawi_glenn]

look at http://en.wikipedia.org/wiki/Angular_momentum_coupling
http://en.wikipedia.org/wiki/Clebsch-Gordan_coefficients

One uses the completness relation, that each set of states constitutes a basis, which you can expand other states into:

$$|a> = \sum_{b'} |b'><b'|a> = \sum_{b'} <b'|a>|b'>$$

 

[malawi_glenn]

how's it going?