Some example solutions: Let's begin with a simple case, the \( 0d_{5/2} \) space containing six single-particle states

For two particles, there are a total of 15 states, which we list here with the total \( M \):

• \( | 1,2 \rangle \), \( M= -4 \), \( | 1,3 \rangle \), \( M= -3 \)
• \( | 1,4 \rangle \), \( M= -2 \), \( | 1,5 \rangle \), \( M= -1 \)
• \( | 1,5 \rangle \), \( M= 0 \), \( | 2,3 \rangle \), \( M= -2 \)
• \( | 2,4 \rangle \), \( M= -1 \), \( | 2,5 \rangle \), \( M= 0 \)
• \( | 2,6 \rangle \), \( M= 1 \), \( | 3,4 \rangle \), \( M= 0 \)
• \( | 3,5 \rangle \), \( M= 1 \), \( | 3,6 \rangle \), \( M= 2 \)
• \( | 4,5 \rangle \), \( M= 2 \), $ | 4,6 \rangle$, \( M= 3 \)
• \( | 5,6 \rangle \), \( M= 4 \)

Of these, there are only 3 states with \( M=0 \).