In class, we talked about the singlet state being given by 1 |0,0>= (l+z,z> |z,+z >) Prove the following: 0 An equivalent representation of the singlet state is ID, 0 >= + w, :I: > --1 $1+$ >)- . Remind yourself that an arbitrary ket 111 >= cosgl + z > +eisingl z >, i.e., go back to earlier chapters in the book and nd the point at which we rst encountered this equation and refresh the context in your memory. An equivalent representation of the singlet state is [0, 0 >2 0 +, > -| ,+ >). Marvel at the magic for a moment. The singlet state looks the same no matter what basis you pick. Next, let us practice taking inner products with kets of multiple spins. Use 173) = cos%\\ +2 > +sin%| z > and [0,0 >= 715-\" +2, 2 > I z,+z >). Compute the following 1-?\" = Sin 6_ |+z7 _ cos a l 27 7. 3. ' 0 (+11, z]0,0) - (+71, +z|0,0) . (71, z|0, 0)