For application in the pairing model we can go further and consider only states with no "broken pairs," that is, if \( +k \) is filled (or \( m = +1/2 \), so is \( -k \) (\( m=-1/2 \)). If you want, you can write your code to accept only these, and obtain the following six states:

• \( | 1, 2 , 3 , 4 \rangle , \)
• \( | 1 , 2 , 5 , 6 \rangle , \)
• \( | 1 , 2 , 7 , 8 \rangle , \)
• \( | 3 , 4 , 5 , 6 \rangle , \)
• \( | 3 , 4 , 7 , 8 \rangle , \)
• \( | 5 , 6 , 7 , 8 \rangle \)