Finding the possible values of Lz

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In summary, the conversation discusses a question about finding the values of Lz and the expectation value of Lz in a given state. The hint given suggests expanding the state in the basis of |l,m_l> and |s,m_s> using a Clebsch-Gordan table. Additional resources are provided for further understanding.
  • #1
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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
 
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  • #2
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)
 
  • #3
thanks lot for your help...Actally I am having some trouble unerstanding this whole conceptI will tr it out.
 
Last edited:
  • #5
how's it going?
 

1. What is Lz in quantum mechanics?

Lz is the z-component of the angular momentum operator in quantum mechanics. It represents the amount of angular momentum in the z-direction of a particle.

2. How do you find the possible values of Lz?

The possible values of Lz can be found by solving the eigenvalue equation for the angular momentum operator, which is given by Lz|ψ> = λ|ψ>, where λ is the eigenvalue and |ψ> is the eigenstate. The eigenvalues are the possible values of Lz.

3. What is the significance of Lz in quantum mechanics?

Lz is a fundamental quantity in quantum mechanics, as it is one of the three components of the angular momentum operator. It is used to describe the rotational motion and orientation of particles, and plays a crucial role in many physical phenomena and applications.

4. Are there any restrictions on the possible values of Lz?

Yes, there are restrictions on the possible values of Lz. In quantum mechanics, Lz can only take on discrete values, which are determined by the quantum numbers of the system. Additionally, the possible values of Lz are limited by the uncertainty principle.

5. How does Lz relate to other quantum mechanical operators?

Lz is related to other quantum mechanical operators, such as the position and momentum operators, through the commutation relations. These relations describe how the operators interact and affect each other in quantum systems.

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