- #1

**=**

*J*

*J*_{1}+

*J*_{2}, with

*j*

_{1}=

*j*

_{2}=1. Find the eigenstates of the total angular momentum I

*jm*> in terms of the product states I

*j*> in two ways

_{1}m_{1}j_{2}m_{2}(a) Make use of the tables of the Clebech _Gordan coefficients

(b) The state with

*m*

_{1}=

*m*

_{2}= 1 must be a state with

*j = m =*2 (why?). Apply

*J*repeatedly to this state to obtain all other states of

_{-}*j = 2.*Form an appropriate linear combination of the two states with

*m*

_{1}+

*m*

_{2}=1 to obtain the state with

*j*=1 , and

*m*=1 . Find the other

*j*= 1 states by applying

*J*

_{-}repeatedly. Finally, find the

*j*=

*m*= 0 state by forming an appropriate linear combination of the three states with

*m*

_{1}+

*m*

_{2}= 0.

(c) Compare the results in (a) and (b).

I don't know how to use Clebech - Gordand coefficients, so please explain details using the table.