kvantliq mexanika 1

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2012 2 i . i . 1-1. . 1-2. . 1-3. . 1-4. - . 1-5. . 1-6. . ii . 1-7. . 1-8 . 1-9. . 1-10. . 1-11. . 1-12. . iii 1-13. . 1-14. . 1-15. . ii . 2-1-1. . 2-1-2. . 2-1-3. . 2-1-4. . 2-1-5. - . 2-2-1. . 2-2-2. . 2-2-3. . 2-2-4. 2-3-1. . 2-3-2. . 2-3-3. . 2-3-4. . 2-3-5. . 2-3-6. . 2-3-7. . 2-3-8. . 2-4-1. . 2-4-2. . 2-4-3. 2-4-4. . 2-4-5. . 2-5-1. . 2-5-2. . 2-5-3. 3 . 2-5-4. . 2-5-5. . 2-6-1. . iii . 3-1. ). 3-2. 3-3. . 3-4. . 3-5. . iv 4-1. . 4-2. . 4-3. . . 5-1. . 5-2. . 5-3. . 5-4. . 5-5. . 5-6. . 5-7. s . 5-8. . 5-9. . 5-10 . 5-11. . vi . 6-1. - . 6-2. . 6-3. . 6-4. …

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.17)- ( , ) (1.5.17)- x = (d /dk) t (1.5.18) . (1.5.18)- v = (d /dk) (1.5.19) v e = p /2m e p k = 2 . (1.5.20) (1.5.20)- k /m p/m v v (1.5.17)- x ). t k = ± x = d dk t ± k . (1.5.21) 15 (1.5.21)- (1.5.20)- 6. | | | | = = + . (1.6.1) (1.5.1)- + , = . * –i (1.6.1)- 2 ( ) + 1 ( ) 2 ( ) . (1.6.2) ( ) = = (1.6.1)- (1.6.2)- 16 | | = 2 ( ) (1.6.3) v s | | = 2 ( ) (1.6.4) "-" ). (1.6.4)- v = 2 ( ) (1.6.5) (1.6.5) (1.6.3)- | | = | | . | | + = 0 (1.6.6) = 0 j [1- (51.1)- ]. (1.6.6)- j (1.6.5)- ( ) + 2 ( ) = 0. (1.6.7) | …

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6 = , ( = 1,2,3), .1) = , ( = 1,2,3), .2) = . .3) ik ik ). ai a ). .1) a aa. .4) .2) a = .5) ’ik ik ki .6) = .7) .6)- .7)- .5) 27 a = a. .8) .8) 7 .8) .2) a a-1a’. .9) .4) .9) .1) .2) b aa, .10) a a-1b. .11) a a b .10) .11) b n .1) .2) = ( = 1,2, … , ), .12) = ( = 1,2, … , ). .13) (a-1 ). = -1 n n = … … … … … … … . .14) .14) 1 28 = ( , ) = … … … … … … … .15) m·n ( )- - ×1 1× - ik ik ), ik ik ). .14) - .15) ik ki .16) . .17) ik - ki .18) . .19) ik 29 = 0 …

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7) (1.9.2) (1.9.5) = (1.9.8)- = = (1.9.4) (1.9.17)- 37 q ( ) = q( ) ( ) (1.9.18) r (r) ). (1.9.18)- |q | q ( ) ( ) |q | q ( ) ( ) q k m a = a (1.9.19) a a . a a a (a ) = (a ) . (1.9.20) a a = a = a (1.9.21) a a a . (1.9.21)- (1.8.7)- a = a = a (1.9.22) a [(1.8.9)- (1.8.10)- ]. (1.9.21)- (1.8.7)- (1.9.9)-, (1.8.7)- (1.8.3)- = | = | = | = . 38 (1.8.7)- (1.9.21)- | = , = . (1.7.9)- | = | = | = , = , = (1.9.23) [(1.7.10)- ]. ~ = , ~ = (1.9.23)- ( …) = . | = (1.9.24) (1.7.7)- (1.9.24)- - ): = ( ) (1.7.14)- = | = , | . | 39 = , (1.9.25) (1.7.14)- - = …

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= ba (1.10.20) (1.10.20)- ab = ba (1.10.21) 45 a b ab ba a, b a, b = ab ba. (1.10.22) (1.10.19)- , = = 1. , ). q = q , (1.10.23) r = r . (1.10.24) (1.10.23) (1.10.24) q + r = (q + r ) (1.10.25) q + r q r + = (1.10.26) 46 (1.10.24)- q (1.10.23)- qr = q = = . (1.10.27) (1.10.26)- (1.10.3)- = qr q q q (1.10.23)- r (1.10.24)- rq = r = . (1.10.27)- qr = rq q r 1) 2) 1)- 2)- 1)- 2)- 2)- 1)- a b ( ) = ( ), (1.10.28) ( ) = ( ) (1.10.29) (1.10.28)- b a b ( ) = ( ) ( ) = ( ) . [ ( )] a a ( ) ( ). ( ) = a ( ) (1.10.29)- a 47 a q r qr qr (1.10.6)- …

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2012 2 i . i . 1-1. . 1-2. . 1-3. . 1-4. - . 1-5. . 1-6. . ii . 1-7. . 1-8 . 1-9. . 1-10. . 1-11. . 1-12. . iii 1-13. . 1-14. . 1-15. . ii . 2-1-1. . 2-1-2. . 2-1-3. . 2-1-4. . 2-1-5. - . 2-2-1. . 2-2-2. . 2-2-3. . 2-2-4. 2-3-1. . 2-3-2. . 2-3-3. . 2-3-4. . 2-3-5. . 2-3-6. . 2-3-7. . 2-3-8. . 2-4-1. . 2-4-2. . 2-4-3. 2-4-4. . 2-4-5. . 2-5-1. . 2-5-2. . 2-5-3. 3 . 2-5-4. . 2-5-5. . 2-6-1. . iii . 3-1. ). 3-2. 3-3. . 3-4. . 3-5. . iv 4-1. . 4-2. . 4-3. . . 5-1. . 5-2. …

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