Конспект лекций по статистической физике. Коренблит С.Э - 107 стр.

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¨ H, á¢ï§ ­­ë¬¨ ãá«®¢¨¥¬ £à ¤¨¥­â­®© ¨­¢ ਠ­â­®á⨠Œ, ª ª [30]:
  Ek   = ikAk ; Hk = i (k  Ak ) ;         Ak = ak (t) exp(ik 
 r);     (11.4)
              a k (t) + !k2ak (t) = 0;    ak (t) = pekV exp( i!k t);
£¤¥ ak (t){ ¥¥ ­®à¬¨à®¢ ­­ ï ­ ®¡ê¥¬ ¬¯«¨â㤠, ek { ¥¤¨­¨ç­ë© ¢¥ª-
â®à ¯®«ïਧ 樨 ¢®«­ë, ®¯à¥¤¥«ïî騩 ­ ¯à ¢«¥­¨ï ª®«¥¡ ­¨© ¢¥ªâ®à®¢
Ak , E k , ¨ Hk , ª ª ¯®¯¥à¥ç­ë¥, ¢ ᨫã (11.2), ª ¢®«­®¢®¬ã ¢¥ªâ®àã k:
(r 
 E k ) / (r 
 Ak ) = i(k
Ak ) = 0, (k
ek ) = 0 = (k
(kek )), â.¥. ¨¬¥-
îâáï ⮫쪮 ¤¢¥ ­¥§ ¢¨á¨¬ë¥ ¯®«ïਧ 樨 ¯«®áª®© ¢®«­ë = 1; 2 ¢ ¯«®á-
ª®áâ¨, ¯¥à¯¥­¤¨ªã«ïà­®© ­ ¯à ¢«¥­¨î à á¯à®áâà ­¥­¨ï ¢®«­ë. ‚®«­
­ §ë¢ ¥âáï «¨­¥©­® ¯®«ïਧ®¢ ­­®©, ¥á«¨ ­ ¯à ¢«¥­¨¥ ª®«¥¡ ­¨© ®áâ -
¥âáï ¯®áâ®ï­­ë¬.  ¯à¨¬¥à, ¤«ï ¢®«­ë, à á¯à®áâà ­ïî饩áï ¢ ­ ¯à -
¢«¥­¨¨ ®á¨ Z , ¯®«ïਧ æ¨ï ¢¤®«ì ®á¥© X ¨ Y § ¤ ¥âáï, ᮮ⢥âá⢥­­®,
¢¥ªâ®à ¬¨ (áà. á (2.20), (2.21)):
                            0 1                  0 1
                            BB 1 CC              BB 0 CC
                     ek1 = B@ 0 CA ;      ek2 = B@ 1 CA :               (11.5)
                              0                    0
‘㯥௮§¨æ¨ï íâ¨å ¤¢ãå «¨­¥©­ëå ¯®«ïਧ 権 c à §«¨ç­ë¬¨ ª®íää¨-
樥­â ¬¨ a; b; jaj2 + jbj2 = 1; ¤ ¥â ¯à ¢®- ¨«¨ «¥¢®í««¨¯â¨ç¥áªãî ¯®«ï-
ਧ æ¨î.  ¯à¨¬¥à, ªà㣮¢®© ¯®«ïਧ 樨 ᮮ⢥âáâ¢ãîâ:
                          0 1                      0 1
                      1   BB 1 C               1   BB 1 CC
                ekR = p2 B@ i CCA ;      ekL = p2 B@ i CA :             (11.6)
                              0                         0
Ž¡é¥¥ à¥è¥­¨¥ ¢®«­®¢®£® ãà ¢­¥­¨ï (11.3) ï¥âáï ¢¥é¥á⢥­­®© á㯥à-
¯®§¨æ¨¥© ¯«®áª¨å ¬®­®å஬ â¨ç¥áª¨å ¯®«ïਧ®¢ ­­ëå í«¥ªâ஬ £­¨â-
­ëå ¢®«­, { ¢®«­®¢ë¬ ¯ ª¥â®¬ E (r; t) (¨, ᮮ⢥âá⢥­­®, ¤«ï H(r; t))
¢¨¤ :
                E (r; t) = i X k [f (k)Ak f (k)Ak ] ;
                              k;
                                                                (11.7)
£¤¥ = 1; 2 ¨«¨ = R; L, ¨ k = k , ¤«ï Œ ¢ ï騪¥ ®¡ê¥¬®¬ V ¯à¨-
­¨¬ ¥â ¤¨áªà¥â­ë¥ §­ 祭¨ï: ¯à¨ ­ «®¦¥­¨¨ ¯¥à¨®¤¨ç¥áª¨å £à ­¨ç­ëå
ãá«®¢¨© ¢¤®«ì ª ¦¤®£® ॡà ï騪 V = L1L2L3 ¤®«¦­® 㪫 ¤ë¢ âìáï
楫®¥ ç¨á«® i = Li=i ¤«¨­ ¢®«­ i , i = 1; 2; 3. ’®£¤ ¢®«­®¢®© ¢¥ªâ®à