Total spin of triplet and singlet states

[K448]

I'm a litte confused about spin triplet and singlet states. How do we know that for ↑↓+↓↑ the total spin S is 1, and for ↑↓-↓↑ the total spin S is 0?
Also, how is total m_s computed for these two states? (I understand that they are both 0, but not sure where that comes from)

Thank you very much for the help!

 

[blue_leaf77]

How do we know that for ↑↓+↓↑ the total spin S is 1, and for ↑↓-↓↑ the total spin S is 0?

Apply the (squared) total spin operator $\mathbf{S}^2 = (\mathbf{S_1}+\mathbf{S_2})^2$ to those states.

Also, how is total ms computed for these two states

Apply the operator $S_z = S_{1z} + S_{2z}$ to those states. Alternatively, upon following the theorem of the addition of angular momenta, you will find that the z component of the resultant spin state is equal to the sum of the z components of the individual states appearing in the resultant state's representation in the individual spin state basis.

 

[K448]

Apply the (squared) total spin operator $\mathbf{S}^2 = (\mathbf{S_1}+\mathbf{S_2})^2$ to those states.

Apply the operator $S_z = S_{1z} + S_{2z}$ to those states. Alternatively, upon following the theorem of the addition of angular momenta, you will find that the z component of the resultant spin state is equal to the sum of the z components of the individual states appearing in the resultant state's representation in the individual spin state basis.

Thank you very much! I realize I never learned the total spin operator... Is there a recommended reading about this?

 

[blue_leaf77]

Introduction to QM by Griffith chapter 4 or Modern QM by Sakurai chapter 3. The latter is more advanced than the former but especially on the addition of angular momenta and it's in fact my favorite QM book, I found it still easy to understand. Alternatively MIT's opencourse material will also do http://ocw.mit.edu/courses/physics/...all-2013/lecture-notes/MIT8_05F13_Chap_10.pdf

 

[K448]

Introduction to QM by Griffith chapter 4 or Modern QM by Sakurai chapter 3. The latter is more advanced than the former but especially on the addition of angular momenta and it's in fact my favorite QM book, I found it still easy to understand. Alternatively MIT's opencourse material will also do http://ocw.mit.edu/courses/physics/...all-2013/lecture-notes/MIT8_05F13_Chap_10.pdf

Thank you! :)