時間部分f(t)⋍e^i√ℓ・t⋍e^i√2k+1・t | |||||||
微分して i√ℓ・f(t)⋍i√2k+1・f(t) | |||||||
∴⓪⋍√ℓ・f(t)⋍√2k+1・f(t) | |||||||
k | 文献値 | 文/11 | +(s/11) | √Q⋍√2k+1 | s | リュカ数列(+β) | |
1 | 14.13472 | 1.284975 | 0.454545 | 1.73952 | 5 | ⋆ | (mod5) |
2 | 21.02203 | 1.911094 | 0.363636 | 2.27473 | 4 | ⋆ | 5+4⋍9-5⋍4 |
3 | 25.01085 | 2.273714 | 0.363636 | 2.63735 | 4 | ⋆ | 4+4⋍8 |
4 | 3 | ⋆ | |||||
5 | 30.42487 | 2.765897 | 0.727273 | 3.49317 | 8 | ⋆ | 4+8⋍12-5⋍7 |
6 | 32.93506 | 2.994096 | 0.636364 | 3.63046 | 7 | ⋆ | 8+7⋍15-10⋍5 |
7 | 37.58617 | 3.416925 | 0.454545 | 3.87147 | 5 | ~ | 7+5⋍12-9⋍3 |
8 | 40.91871 | 3.719883 | 0.272727 | 3.99261 | 3 | ~ | 5+3⋍8ー3⋍5 |
9 | 43.32707 | 3.938825 | 0.454545 | 4.39337 | 5 | ~ | 3+5⋍8ー3⋍5 |
10 | 4.58257569 | ⋆ | |||||
11 | 48.00515 | 4.364105 | 0.454545 | 4.81865 | 5 | ~ | 5+5⋍10-6⋍4 |
12 | 49.77383 | 4.524894 | 0.363636 | 4.88853 | 4 | ~ | 5+4⋍9-4⋍5 |
13 | 52.97 | 4.815455 | 0.454545 | 5.27 | 5 | ~ | 4+5⋍9-4⋍5 |
14 | 56.446 | 5.131455 | 0.454545 | 5.586 | 5 | ~ | 5+5⋍10-8⋍2 |
15 | 59.347 | 5.395182 | 0.181818 | 5.577 | 2 | ~ | 5+2⋍7-6⋍1 |
16 | 60.831 | 5.530091 | 0.090909 | 5.621 | 1 | ⋆ | 2+1⋍3 |
17 | 5.91607978 | ⋆ | |||||
18 | 65.112 | 5.919273 | 0.272727 | 6.192 | 3 | ⋆ | 1+4⋍5⋍10 |
29 | 7.61577311 | ⋆ | |||||
30 | 75.8 | 6.890909 | 0.909091 | 7.8 | 10 | ⋆ | … |
⓪Hψ⋍-iaψ/at (シュレデインガ-) | ∴2s+1三p (mod 4) | |||||||
時間部分f(t)⋍e^i√ℓ・t⋍e^i√2k+1・t | ガウス素数p→4n+1,4n+3 | |||||||
微分して i√ℓ・f(t)⋍i√2k+1・f(t) | ∴2s+1三p (mod 4) | |||||||
∴⓪⋍√ℓ・f(t)⋍√2k+1・f(t) | Σ⋍ | ガウスp | ||||||
k | 文献値 | 文/11 | +(s/11) | √Q⋍√2k+1 | s | s+1 | 2s+1 | mod 4 |
1 | 14.13472 | 1.284975 | 0.454545 | 1.73952 | 5 | 6 | 11 | 3 |
2 | 21.02203 | 1.911094 | 0.363636 | 2.27473 | 4 | 5 | 9 | 1 |
3 | 25.01085 | 2.273714 | 0.363636 | 2.63735 | 4 | 5 | 9 | 1 |
4 | 3 | 0 | 1 | 1 | 1 | |||
5 | 30.42487 | 2.765897 | 0.727273 | 3.49317 | 8 | 9 | 17 | 1 |
6 | 32.93506 | 2.994096 | 0.636364 | 3.63046 | 7 | 8 | 15 | 3 |
7 | 37.58617 | 3.416925 | 0.454545 | 3.87147 | 5 | 6 | 11 | 3 |
8 | 40.91871 | 3.719883 | 0.272727 | 3.99261 | 3 | 4 | 7 | 3 |
9 | 43.32707 | 3.938825 | 0.454545 | 4.39337 | 5 | 6 | 11 | 3 |
10 | 4.58257569 | 0 | 1 | 1 | 1 | |||
11 | 48.00515 | 4.364105 | 0.454545 | 4.81865 | 5 | 6 | 11 | 3 |
12 | 49.77383 | 4.524894 | 0.363636 | 4.88853 | 4 | 5 | 9 | 1 |
13 | 52.97 | 4.815455 | 0.454545 | 5.27 | 5 | 6 | 11 | 3 |
14 | 56.446 | 5.131455 | 0.454545 | 5.586 | 5 | 6 | 11 | 3 |
15 | 59.347 | 5.395182 | 0.181818 | 5.577 | 2 | 3 | 5 | 1 |
16 | 60.831 | 5.530091 | 0.090909 | 5.621 | 1 | 2 | 3 | 3 |
17 | 5.91607978 | 0 | 1 | 1 | 1 | |||
18 | 65.112 | 5.919273 | 0.272727 | 6.192 | 3 | 4 | 7 | 3 |
29 | 7.61577311 | 0 | 1 | 1 | 1 | |||
30 | 75.8 | 6.890909 | 0.909091 | 7.8 | 10 | 11 | 21 | 1 |
⓪Hψ⋍-iaψ/at (シュレデインガ-) | ||||
時間部分f(t)⋍e^i√ℓ・t⋍e^i√2k+1・t | ||||
微分して i√ℓ・f(t)⋍i√2k+1・f(t) | ||||
∴⓪⋍√ℓ・f(t)⋍√2k+1・f(t) | ||||
k | 文献値 | 文/11 | +(s/11) | √Q⋍√2k+1 |
1 | 14.13472 | 1.284975 | 0.454545 | 1.73952 |
2 | 21.02203 | 1.911094 | 0.363636 | 2.27473 |
3 | 25.01085 | 2.273714 | 0.363636 | 2.63735 |
4 | 3 | |||
5 | 30.42487 | 2.765897 | 0.727273 | 3.49317 |
6 | 32.93506 | 2.994096 | 0.636364 | 3.63046 |
7 | 37.58617 | 3.416925 | 0.454545 | 3.87147 |
8 | 40.91871 | 3.719883 | 0.272727 | 3.99261 |
9 | 43.32707 | 3.938825 | 0.454545 | 4.39337 |
10 | 4.58257569 | |||
11 | 48.00515 | 4.364105 | 0.454545 | 4.81865 |
12 | 49.77383 | 4.524894 | 0.363636 | 4.88853 |
13 | 52.97 | 4.815455 | 0.454545 | 5.27 |
14 | 56.446 | 5.131455 | 0.454545 | 5.586 |
15 | 59.347 | 5.395182 | 0.181818 | 5.577 |
16 | 60.831 | 5.530091 | 0.090909 | 5.621 |
17 | 5.91607978 | |||
18 | 65.112 | 5.919273 | 0.272727 | 6.192 |
29 | 7.61577311 | |||
30 | 75.8 | 6.890909 | 0.909091 | 7.8 |
ルジャンド | ℓ^2+ℓ⋍α^2+α | |||||||||||
∵Δ(M)⋍ℓ^2⋍(2k+1)^2 (同形) | △(m) | ⋍ | 2k+1 | |||||||||
∴△ | ⋍ | 4k^2+4k+1 | ⋍ | ℓ^2 | 質量項 | ⋍ | ℓ | |||||
(M行列) | 1 | 2 | Δ⋍ | 9 | (m) | 0 | √3 | Δ⋍ | 3 | |||
M1⋍ | -2 | 5 | m1⋍ | -√3 | 0 | |||||||
(M行列) | 1 | 4 | Δ⋍ | 25 | (m) | 0 | √5 | Δ⋍ | 5 | |||
M2⋍ | -4 | 9 | m2⋍ | -√5 | 0 | |||||||
(M行列) | 1 | 6 | Δ⋍ | 49 | (m) | 0 | √7 | Δ⋍ | 7 | |||
M3⋍ | -6 | 13 | m3⋍ | -√7 | 0 | |||||||
(M行列ツ) | 1 | 8 | Δ⋍ | 81 | (m) | 0 | √9 | Δ⋍ | 9 | |||
M4⋍ | -8 | 17 | m4⋍ | -√9 | 0 | |||||||
(M行列) | 1 | 10 | Δ⋍ | 121 | (m) | 0 | √11 | Δ⋍ | 11 | |||
M5⋍ | -10 | 21 | m5⋍ | -√11 | 0 | |||||||
(M行列) | 1 | 2k | Δ⋍ | 4k^2+4k+ | (m) | 0 | √2k+1 | Δ⋍ | 2k+1 | |||
Mk⋍ | - | 2k | 4k+(4Q+1) | mk⋍ | - | √2k+1 | 0 |