Discover the Spin of an Electron Using Angular Momentum Operator and Eigenvalues

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Homework Help Overview

The discussion revolves around the calculation of the spin of an electron using the angular momentum operator and its eigenvalues. Participants are exploring the relationship between total angular momentum, orbital angular momentum, and spin in quantum mechanics.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to understand how to derive the spin of the electron from the eigenvalues of the angular momentum operator. There is discussion about the equation J^2 = L^2 + S^2 + 2L·S and how to manipulate it to isolate the spin S.

Discussion Status

Some participants are seeking clarification on the problem statement and the specific requirements for demonstrating the spin of the electron. There is an acknowledgment of the need to refer to the original problem text for better context. Multiple interpretations of the equations involved are being explored.

Contextual Notes

Participants have noted the importance of the eigenvalues of the angular momentum operator and the need for precise problem statements to guide their reasoning. There is an emphasis on ensuring all relevant details are considered in the discussion.

rubertoda
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I should Use
the fact that in general the eigenvalues of the square of the angular momentum
operator is J(J + 1)h and show the spin of the electron.

I have J= L+S and J2 = L2+ S2

Homework Statement




But how could i find the spin of the electron
 
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Not really, J^2 = L^2 + S^2 +2 L.S. And post the whole text of your problem.
 
dextercioby said:
Not really, J^2 = L^2 + S^2 +2 L.S. And post the whole text of your problem.
Yes, i was sloppy. I meant that. But, I am asked to show the spin of the electron, by knowing that the eigenvalue of J2 is usually J(J+1)hbar...what do they mean?

sthg like solving for S in J^2 = L^2 + S^2 +2 L.S?
 
rubertoda said:
Yes, i was sloppy. I meant that. But, I am asked to show the spin of the electron, by knowing that the eigenvalue of J2 is usually J(J+1)hbar2...what do they mean?

sthg like solving for S in J^2 = L^2 + S^2 +2 L.S?

So how to do this
 
Can you, please, post the text of your problem, exactly as it appears in your book ?
 
Calculate the square of the total spin operator and find all its eigenvalues. Use
the fact that in general the eigenvalues of the square of the angular momentum
operator is J(J + 1)¯h
2
to find the spin of the electron.



the firts one i have fixed..
 

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