Документ взят из кэша поисковой машины. Адрес оригинального документа : http://hep.phys.msu.ru/4studs/quantum/2008/qm08_2.pdf Дата изменения: Mon Dec 8 08:37:01 2008 Дата индексирования: Mon Oct 1 19:51:50 2012 Кодировка:

(I I ) 2009 . 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. . -. . 19. . . ls-. 1


20. - . , . 21. - . . . 22. , . . 23. , . . 24. . . 25. . . 26. . . . . . 27. , , , , . 28. , . 29. . 1- 2- , . . 3- , . 30. . -. . 31. . . . . . 32. . . , , 1- . 33. . , . , . 34. , , . . . 35. , . 36. . . 37. . . . 38. . . 39. . . . 40. . -. . . 41. . . 42. . - . . 43. . . 44. . .

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1. f (b + a · ). ^^ ^ ^ ^ ^ 2. , [A, B ] = -iB exp(z A)B exp(-z A) = iB . z. 3. exp(i^x )py z exp(-i^x ). l ^^ l 4. 1/2 = ^ 1 7 1 1+i 1-i 6

, , ±1/2 sx , sx , sy , sz . 5. 1/2 = (1/2) + (1/2) · n(, ) ^ - , z . . , ? ? 6. = (1/3) 2 |0 0| + |1 1| + i |0 1| - i |1 0| ^ , . 7. | = (1/ 3) | - | + i| , , , . 8. = ^ 1 1 1 1 1 | | + | | + | | + | | + | | 3 3 3 9 9

, , , . 9. . |xp| - |x| |p| ^^ ^ ^ |px| - |x| |p| ^^ ^ ^ 10. . |x| , |p| . ^ ^ | - | ? 11. | . 3


12. V (x) = -V0 (x - a) - V0 (x + a) + U0 (a - |x|) ((x > 0) = 1, (x < 0) = 0). 13. V (x) = |x| > a, V (x) = 0 b < |x| < a, V (x) = U0 |x| < b. 14. V (x) = V0 (x) + U0 (x) ((x > 0) = 1, (x < 0) = 0). 15.


V (x) =
n=-

V0 (x - na)

16. V (x < 0) = , V (x > 0) = k x2 /2. . 17. - -. 18. . 19. V (r) = -V0 (r - a). 20. - V (r) = -U0 (a - r) + V0 (r - a) ((x > 0) = 1, (x < 0) = 0). 21. V (r < a) = , V (r > c) = , V (a < r < b) = A/r2 , V (b < r < c) = 0. 22. , , 1/r3 , |nlm . 23. 1/2. S = 1, Sz = 0|s(2) |S = 1, Sz = 1 x S = 0, Sz = 0|s
(1) z

S = 1, Sz = -1|s |S = 1 , S z = 0

(2) y

| S = 0 , Sz = 0

24. . 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 25. . 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 ~~ 26. 1/2 |j lsmj . n(, ) (r, , ). 4


27. 1/2 H = p2 /(2m) + V (r) + U (r) l · s V (r) = -V0 (r - a), U (r < a) = -U0 , U (r > a) = 0. . 28. 1/2, , ^ H = -2µ1 s1 H - 2µ2 s2 H + s1 · s2 . 29. 1/2 | = exp(i1 s1x ) exp(i2 s2y ) | , . 30. , A -- , l m |A|lm = l l m
m

a(l)

.. l, m, m. 31. , A -- , lm|A |lm = lm|l |lm lm |A · l |lm /l(l + 1)

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

33. C 1/2 H (t) = (H1 cos t, H1 sin t, H0 ) t = 0 . t. 34. t = 0 . 0 < t < t0 f (t) = f0 . n- t. 35. t = 0 | . t. t. 36. 1/2 ^ H = -2µ0 (s
(1) z

-s

(2) z

)H

z

, t, t = 0 x, -- x. 5


37. , z . E (0) = 3Ї , h . 38. . E (0) = 2Ї , h HI = xy . . 39. , , . . 40. , , . . 41. ( --). 42. n = 2 . 43. n = 2 . 44. n = 2 . 45. n = 2 . 46. n = 2 . 47. n = 2 . 48. 2p3 . 49. 3d2 . 50. 2p3 . 51. 2p4 . 52. , S, L, J nlk . 53. . 54. . 55. . 56. µ- . 1s. 57. a , - a. 58. a , - a. 59. s- V (r) = V0 (r - a). 60. s- V (r) = V0 (r - a). . 6


61. V (r < a) = -V0 , V (r > a) = 0. . 62. A/r2 . . 63. V (r < a) = A/r2 , V (r > a) = 0. 64. V (r) = -U0 (a - r) + V0 (r - a) ((x > 0) = 1, (x < 0) = 0). 65. . 66. , H 3 , , 1s H e3+ - . 67. . |001 . W (x, y ) = W0 (x - y ). 68. µ- . 1s 2s. 69. |k,p . 70. |k1 ,p1 , k2 ,p2 . 71. | = |k1 ,p1 / 2 + |k2 ,p2 / 2. 72. . 73. . 74. , . . . 75. 2p1/2 (c ). 76. 2p3/2 (c ). 77. . 3d 2p ( ). . 78. 1/2 H . . 79. . 80. , S S .

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