Proof of some identities regarding spin angular momentum.

[Faisal Moshiur]

If we define Si=(1/2)× (reduced Planck's const)×sigma
Then what will be (sigma dot vect{A})multiplied by (Sigma dot vect{B})
Here (sigma)i is Pauli matrix.
Next one is, what will we get from simplifying
<Alpha|vect{S}|Alpha> where vect{S} is spin vector & |Apha>is equal to " exp[{i×(vect{S} dot (n_hat))× Theta/(reduced Planck's const)}]

 

[dextercioby]

If we define Si=(1/2)× (reduced Planck's const)×sigma
Then what will be (sigma dot vect{A})multiplied by (Sigma dot vect{B})
Here (sigma)i is Pauli matrix.
Next one is, what will we get from simplifying
<Alpha|vect{S}|Alpha> where vect{S} is spin vector & |Apha>is equal to " exp[{i×(vect{S} dot (n_hat))× Theta/(reduced Planck's const)}]

Well, first help your reader by learning how to use LaTex. This is very easy and we have a tutorial on this forum. Then what is "multiplied" ?

 

[jtbell]

Well, first help your reader by learning how to use LaTex. This is very easy and we have a tutorial on this forum.

Namely, here: https://www.physicsforums.com/help/latexhelp/

To start you off, the code S_i = \frac 1 2 \hbar \sigma enclosed in the appropriate delimiters (as described in the link above) produces $$S_i = \frac 1 2 \hbar \sigma$$ Is this what you intended to write for your first equation?