Let $$\left| n \right\rangle $$ and $$\left| p \right\rangle $$ denote the isospin state with $$I = \frac{1}{2},\,{I_3} = \frac{1}{2}$$   and $$I = \frac{1}{2},\,{I_3} = - \frac{1}{2}$$   of a nucleon respectively. Which one of the following two-nucleon states has $$I = 0,\,{I_3} = 0\,?$$

Let $$\left| n \right\rangle $$ and $$\left| p \right\rangle $$ denote the isospin state with $$I = \frac{1}{2},\,{I_3} = \frac{1}{2}$$   and $$I = \frac{1}{2},\,{I_3} = - \frac{1}{2}$$   of a nucleon respectively. Which one of the following two-nucleon states has $$I = 0,\,{I_3} = 0\,?$$ Correct Answer $$\frac{1}{{\sqrt 2 }}\left( {\left| {np} \right\rangle - \left| {pn} \right\rangle } \right)$$

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