Spin Quantum # in Triplet state

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SUMMARY

The discussion focuses on the properties of two spin 1/2 identical particles in quantum mechanics, specifically regarding the triplet and singlet states. The triplet state consists of three configurations: |UP,UP>, 1/√2 (|UP,DOWN> + |DOWN,UP>), and |DOWN,DOWN>. In the triplet state, the configurations |UP,UP> and |DOWN,DOWN> indicate that the two electrons possess the same spin quantum number, while the middle configuration represents differing spin quantum numbers. In contrast, the singlet state features two spin quantum numbers with the same total spin (s²) but differing z-components (s_z).

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phys_student1
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Hello,

For two spin 1/2 identical particles, the triplet state is:

|UP,UP>
1/√2 (|UP,DOWN> + |DOWN,UP>)
|DOWN,DOWN>

Q1: in the up,up or down,down, are the two electrons considered to have the same spin quantum number?

Q2: If so, then only the middle one (see above) is where they have different spin quantum numbers, right?

Q3: In the Singlet state, they have different spin quantum numbers, right?
 
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The are two spin Q numbers. They have the same s^2, but different s_z.
 

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