normalise form of state AComplete the following about the two states,

$|A$:

$($i$)$ Give the normalised form of the state $|A$:$.$

$($ii$)$ Given that hat$(S{)}_z|m_S$:$,$ prove that the state $|B$: either is$,$ or is not, an

eigenfunction of the Hamiltonian operator widehat$(H)=$Dhat$(S{)}_z^2.$