Документ взят из кэша поисковой машины. Адрес оригинального документа : http://hep.phys.msu.ru/4studs/quantum/2010/zach10.pdf Дата изменения: Mon May 17 08:20:39 2010 Дата индексирования: Mon Oct 1 19:52:15 2012 Кодировка: Поисковые слова: m 2

" " (I I ) 2010 . ( , .) http://hep.phys.msu.ru http://hepqt.itpm.msu.su

1. . . , . . 2. . . . . 3. . , , . 4. . . . , . 5. . . . 6. . . . 7. "" . "" (, , ). "" GHZ (Greenberger, Horne, Zeilinger). 8. , , . 9. . . . , . 10. . . . 11. . , , . . . 12. . . 13. , . . 14. . . . 15. -. . . 16. 3- . , . . 17. . . . . 18. . -. . 20. - . , . 21. - . . . 1. 2. 3. 4. f (b + a · ). ^^ ^ ^ ^ ^ , [A, B ] = -iB exp(z A)B exp(-z A) = iB . z. ^x )py z exp(-i^x ). exp(il ^ ^ l exp(i^x ) · exp(iapy ) · exp(-i^x ) l ^ l

5. . exp a+ a · x · exp -a+ a ^^ ^ ^^ 6. . exp (a+ ay - a+ ax ) · x · exp - (a+ ay - a+ ax ) ^x ^ ^y ^ ^ ^x ^ ^y ^ 1


-- 7. 1/2 1 | = 7 1-i 2+i

(=?, =?). , n ( , ). n ( , ). , . 8. 1/2 | = exp[i( /2)(- sin 1 + cos 2 )] 1 0

(=?, =?). , n ( , ). n ( , ). , . 9. 1/2 = (1/2) + (1/2) · n(, ) ^ - , z . . , ? ? 10. 1/2 1/4 1/8 - i/8 = 1/8 + i/8 3/4 . - , n ( , ). n ( , ). , . 11. 1/2, x, - z . Hz , . - x. . -- 12. = (1/3) 2 |0 0| + |1 1| + i |0 1| - i |1 0| ^ , . 13. . |xp| - |x| |p| ^^ ^ ^ |px| - |x| |p| ^^ ^ ^ 14. . |x| , |p| . | - | ? ^ ^ 15. . | . 16. . n|x 4 |n ^ 17. . n|p 4 |n ^ 2 n|p 3 |m ^ n|x 3 |m ^


18. | =
n=0

exp(-n)

1 - exp(-2) |n

. 19. = ^
n=0

exp(-n) 1 - exp(-) |n n|

. 20. 1 1 | = | + | 2 2 | 1, . 21. H= p2 p2 k x2 qy2 y x + + + + xy 2m 2m 2 2

-- 22. V (x) = -V0 (x - a) - V0 (x + a) + U0 (a - |x|) ((x > 0) = 1, (x < 0) = 0). 23. V (x) = |x| > a, V (x) = 0 b < |x| < a, V (x) = U0 |x| < b. 24. V0 (x - c) V (x) = U0 25. x < -a V (x) = V0 (x + b) + V0 (x - b) -a < x < a x>a 26. x < -a 0 V (x) = -U0 + V0 (x) -a < x < a 0 x>a 27. V (x) = -V0 (x - a) - V0 (x + a) 28. x<0 V (x) = -U0 + V0 (x - a) 0 < x < a 0 x>a 3 xb


29. V (x) = V0 (x) + U0 (x) (x < 0) = 0). -- 30.


((x > 0) = 1,

V (x) =
n=-

V0 (x - na)

31. V (x < 0) = , V (x > 0) = k x2 /2. . 32. V (x < 0) = 0, V (0 < x < a) = U0 x/a, V (a < x) = U0 . a 0. 33. - -. 34. . -- 35. 36. (x < 0) = 0). 37. 38. V (r) = -V0 (r - a). - V (r) = -U0 (a - r) + V0 (r - a) ((x > 0) = 1, V (r < a) = , V (r > c) = , V (a < r < b) = A/r2 , V (b < r < c) = 0. - l = 0: 0 V (r ) = V0 r a b r < < < > a r
39. - l = 0: V (r) = V0 (r - a) r < b r>b

40. - l = 0: V (r) = -U0 A/r2 ra

41. - : A/r2 r < a V (r) = A/a2 a < r < b r>b 42. , , 1/r3 , |nlm . -- 43. l m |lx ly |lm 44. | = exp(ilx )|lm 4 l m |ly lx |lm


|ly | 45. 1/2 | = exp(iSx )| PS =1,Sz =1 , 46. 1/2 , n( 47. PS =1,Sz =0 , PS =1,Sz =-1 ? S = 0. - , ). 4 (,,,). 1/2
z
(1)

^ H = -2µ1 s

Hz - 2µ2 s

z

(2)

Hz + s

(1)

·s

(2)

. 48. i 1 1 | = | + | - | 3 3 3 , 0. 49. = ^ 1 1 1 1 1 | | + | | + | | + | | + | | 3 3 3 9 9

, 1. 50. 1 1 | = exp(iSx )| + exp(i Sy )(| - | ) 2 2 , 1. 51. 1/2. S = 1 , Sz = 0 | s
(2) x

| S = 1 , Sz = 1 S = 0 , Sz = 0 | s
(1) z

S = 1, Sz = -1|s(2) |S = 0, Sz = 0 y | S = 1 , Sz = 0

52. . j = l - 1/2, mj = m + 1/2|sy |j = l - 1/2, mj = m - 1/2 j = l + 1/2, mj = m - 1/2|sx |j = l - 1/2, mj = m + 1/2 j = l + 1/2, mj = m + 1/2|sz |j = l - 1/2, mj = m + 1/2 53. . j = l - 1/2, mj = m + 1/2|lx |j = l - 1/2, mj = m - 1/2 j = l + 1/2, mj = m - 1/2|ly |j = l - 1/2, mj = m + 1/2 j = l + 1/2, mj = m + 1/2|lz |j = l - 1/2, mj = m + 1/2 ~~ 54. 1/2 |j lsmj . n(, ) (r, , ). 55. , A -- , l m |A|lm = l l
mm

a(l)

.. l, m, m. 5


56. l1 = 2 l2 = 1. |L = 1, M = 1 | L = 1, M = 0 | L = 1 , M = -1

57. l1 = 1 l2 = 1. . -- 58. C 1/2 H (t) = (H1 cos t, H1 sin t, H0 ) t = 0 . t. t = 0 . 0 < t < t0 f (t) = f0 . n- t. |0 . 0 < t < 2 / f (t) = f0 sin(t). | (t) |n t. t = 0 | . t. t. 1/2 ^ H = -2µ0 (s
(1) z

59.

60.

61.

62.

-s

(2) z

)H

z

, t, t = 0 x, -- x. 63. 1 i 1 | (t = 0) = |10 + |01 + |00 3 3 3 | (t) , x, y , px , py t. 64. (t = 0) = 1 1 1 1 |0 0| + |1 0| + |0 1| + |1 1| 2 4 4 2

, t.

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