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J0(x) = (2/pi) (integrate from 0 to infinity) sin (x . cos ht) dt } N0(x) = (-2/pi) (integrate from 0 to infinity) cos (x cos ht) dt }
i H(1)0 (x) = (2/pi) (integrate from 0 to infinity) ei x cos ht dt = i J0(x) - N0(x)
y(x) = (2/pi) (integrate from 0 to i(pi/2)) cos (x cos ht) dt = y'(x) = (2/pi) (integrate form 0 to i(pi/2)) -sin (x cos ht) d(sin ht)
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| July 8, '49 | ||
|---|---|---|
| (aK F) (N1, N2, ..., NK, ...) = F (N1, N2, ..., NK + 1, ...) (square root of (NK + 1)) | aK | annihilation operator |
| (aK* F) (N1, N2, ..., NK, ...) = F (N1, N2, ..., NK - 1, ...) (square root of (NK)) | aK* | creation operator |
| aK* F = NK F | aK*aK = NK | aKaK* = NK + 1 |
| [aK, aK*] = 1 | See the other commutators vanish. | |
| qK = (square root of ([h?]/(2wK))) (aK + a-K*) | ||
| pK = (square root of (([h?]wK)/2)) [.~?] (aK* - a-K) | ||
| [qK, q-K] = ([h?]/(2wK)) (1 - 1) = 0 | ||
| Unperturbed energy | ||
| H[°?] = ∫V d3 x H[°?] = (1/2)([∑?]KpK*pK) + (1/2)([∑?]K(K2 + [M or U or N?]2))qK*qK | ||
| Choose wK = (square root of ([M or U or N?]2 + K2)) . | ||
| H[°?] = ([h?]/2) ([∑?]K) wK (aK*aK + aKaK*) = (([∑?]K)) ([h?]wK) (NK + (1/2)) | There is zero pt. magy. |
