Table 3: Exact eigenvalues for different values of 𝑙 and 𝑤 𝑎 2 in the case Δ 3 = 0 .

𝑛 𝑙 𝑤 𝑎 2 Conditions 𝐸 𝑛 , 𝑙 𝐸 𝑤 𝑎 2 𝑛 , 𝑙 ( 𝜇 , 𝑔 )

2−1 1 / 2 𝜇 1 = 6 . 3 0 1 8 7 0 8 7 8 9 9 4 1 9 8 𝐸 1 / 2 2 , 1 = 6 . 0 5 1 8 7 0 8 7 8 9 9 4 1 9 8
𝑔 1 = 7 7 . 2 2 2 9 3 0 9 7 0 4 8 6 0 9
𝜇 2 = 2 . 4 8 5 5 3 6 5 0 8 2 1 0 8 5 9 4 𝐸 1 / 2 2 , 1 = 2 . 2 3 5 5 3 6 5 0 8 2 1 0 8 5 9 4
𝑔 2 = 2 4 . 6 0 5 5 7 4 2 7 4 7 0 3 3 3 3

1 𝜇 1 = 7 . 3 9 8 1 8 2 9 8 4 3 2 6 8 7 6 𝐸 1 2 , 1 = 7 . 1 4 8 1 8 2 9 8 4 3 2 6 8 7 6
𝑔 1 = 9 7 . 7 2 4 0 2 6 3 9 1 2 1 8 1
𝜇 2 = 3 . 3 5 5 0 5 7 9 0 1 4 9 6 8 1 9 4 𝐸 1 2 , 1 = 3 . 1 0 5 0 5 7 9 0 1 4 9 6 8 1 9 4
𝑔 2 = 3 4 . 0 3 1 7 0 3 0 2 9 8 8 0 3 3
𝜇 3 = 0 . 9 4 9 8 1 0 5 4 1 7 5 7 4 7 5 6 𝐸 2 2 , 1 = 1 . 1 9 9 8 1 0 5 4 1 7 5 7 4 7 5 6
𝑔 3 = 2 . 1 5 3 0 8 7 3 5 6 4 4 6 2 5 1 4

3/2 𝜇 1 = 8 . 4 6 9 6 2 3 3 4 1 1 2 4 4 1 4 𝐸 3 / 2 2 , 1 = 8 . 2 1 9 6 2 3 3 4 1 1 2 4 4 1 4
𝑔 1 = 1 2 0 . 0 8 2 6 3 6 2 4 6 1 4 1 5 6
𝜇 2 = 4 . 2 7 7 5 0 5 2 1 2 1 6 5 0 4 𝐸 1 2 , 1 = 4 . 0 2 7 5 0 5 2 1 2 1 6 5 0 4
𝑔 2 = 4 5 . 6 8 4 5 7 6 9 0 0 9 2 4 2 8 4
𝜇 3 = 0 . 9 2 8 2 6 5 3 6 0 1 7 5 7 6 1 3 𝐸 1 2 , 1 = 1 . 1 7 8 2 6 5 3 6 0 1 7 5 7 6 1 3
𝑔 3 = 2 . 2 2 0 3 4 9 7 7 8 0 2 3 4 2 9 4

2 𝜇 1 = 9 . 5 2 5 1 2 2 1 1 5 0 6 5 3 8 6 𝐸 2 2 , 1 = 9 . 2 7 5 1 2 2 1 1 5 0 6 5 3 8 3
𝑔 1 = 1 4 4 . 3 5 3 5 6 1 8 8 2 2 3 4 6 3
𝜇 2 = 5 . 2 2 6 9 4 2 1 7 9 9 1 1 1 4 5 𝐸 2 2 , 1 = 4 . 9 7 6 9 4 2 1 7 9 9 1 1 1 4 5
𝑔 2 = 5 9 . 4 5 5 6 3 5 4 5 1 6 8 9 9 9
𝜇 3 = 0 . 9 1 8 6 5 0 8 1 6 9 8 5 9 2 4 4 𝐸 2 2 , 1 = 1 . 1 6 8 6 5 0 8 1 6 9 8 5 9 2 4 4
𝑔 3 = 2 . 2 5 0 6 6 5 2 3 8 6 1 9 2 8 4

201/2 𝜇 1 = 8 . 0 3 2 2 4 3 0 2 3 4 3 8 4 6 3 𝐸 2 2 , 1 = 7 . 2 8 2 2 4 3 0 2 3 4 3 8 4 6 3
𝑔 1 = 1 1 0 . 6 7 8 1 4 3 1 0 4 7 6 8 1 8
𝜇 2 = 4 . 3 2 8 2 5 4 7 0 6 1 2 1 8 2 𝐸 2 , 1 = 3 . 5 7 8 2 5 4 7 0 6 1 2 1 8 2
𝑔 2 = 4 6 . 3 7 5 0 6 2 3 3 1 6 7 4 7 8

2 𝜇 1 = 1 1 . 3 0 7 7 3 7 2 5 9 7 7 3 4 6 1 𝐸 2 2 , 1 = 1 0 . 5 5 7 7 3 7 2 5 9 7 7 3 4 6 1
𝑔 1 = 1 9 0 . 4 0 3 6 0 8 2 3 4 9 3 6 3
𝜇 2 = 7 . 1 8 0 5 6 4 9 0 5 7 0 3 8 6 7 𝐸 2 2 , 1 = 6 . 4 3 0 5 6 4 9 0 5 7 0 3 8 6 7
𝑔 2 = 9 3 . 4 6 3 3 3 6 8 9 3 5 4 5 3 3
𝜇 3 = 0 . 9 4 7 2 0 0 9 1 0 1 3 9 3 0 3 3 𝐸 2 2 , 1 = 1 . 6 9 7 2 0 0 9 1 0 1 3 9 3 0 3 3
𝑔 3 = 2 . 1 6 1 1 8 5 0 1 3 4 7 2 2 0 8 4