Apply the (squared) total spin operator ##\mathbf{S}^2 = (\mathbf{S_1}+\mathbf{S_2})^2## to those states.K448 said:How do we know that for ↑↓+↓↑ the total spin S is 1, and for ↑↓-↓↑ the total spin S is 0?
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 said:Also, how is total ms computed for these two states
Thank you very much! I realize I never learned the total spin operator... Is there a recommended reading about this?blue_leaf77 said: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! :)blue_leaf77 said: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
The total spin of a state refers to the sum of the spin of all the particles in that state. In a triplet state, the total spin is equal to 1, while in a singlet state, the total spin is equal to 0. This means that triplet states have spin quantum numbers of 1, 0, or -1, while singlet states have a spin quantum number of 0.
2.In a triplet state, the electron spins are parallel to each other, meaning they have the same direction. In a singlet state, the electron spins are antiparallel, meaning they have opposite directions. This difference in spin configurations is what leads to the difference in total spin between the two states.
3.Triplet and singlet states are important in quantum mechanics because they play a crucial role in determining the properties of molecules and their chemical reactions. These states are also used in various experimental techniques, such as electron spin resonance, to study the electronic properties of materials.
4.Yes, triplet and singlet states can be interconverted through a process called spin flipping. This occurs when the spin orientation of an electron changes, resulting in a change of state from triplet to singlet or vice versa.
5.The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers. In the case of triplet and singlet states, this principle is evident in the fact that the spin quantum numbers for each state are different, resulting in different electronic configurations. This principle also explains why only two electrons can occupy each orbital, as they must have opposite spins to avoid violating the exclusion principle.