Диссертация (1097858), страница 11

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')? %5595% %632χ (r) = e+ A(k )e]Θ(−z) ,F34GB(k )e Θ(z) + [e1 = (K + k ) − V ,F3"G2?-k − iγ2k,B(k ) =,γ = 2V − k ,A(k ) =F3>Gk + iγk + iγ √2V ≥ k ≥ 0 -- OdN dec.r‚ %:, %<56:, 76 @< -5' 95% %55 1% 8 &%6E :&5'' 5D (@<D F34G 5& V = ∞E &% -%χ (r) = 2esin(k z)Θ(−z).F3/G%'' -DA? %6 :5%DA?  % 95@%  : 56 k = (K, k ) 9?, E = (K + k )/2 00iKRkz2k2zF−γzikz z−ikz z0zzzzz0z0z2zz0kiKRzzk22z#!!%<5 F3!G %6(+)χk (r)= eiKR54ikz z−ikz zikz z αz+ R(kz )e]Θ(z) + D(kz )e e Θ(−z)[e45(−)iKRikz zikz z−ikz z αze Θ(z) + [A1(kz )eχk (r) = e+ A2 (kz )e]e Θ(−z)(kz < 0),F30G(kz > 0),F32G?-kz − kz + iα2kz,D(k,R(kz ) =)=zkz + kz − iαkz + kz − iαkz + kz + iαkz − kz − iαA1(kz ) =,A2 (kz ) =,2kz2kzkz2 + 2V0 + [(kz2 + 2V0)2 + 4V0i2 ]1/2V0i,α= .(kz )2|kz |ZgW`-6 ' &%6 V %<5kz =F3=G0iV = (−V0 + iV0i )Θ(−z)- -5' &% )%' 95%: 5 %55E 755? .? < 5& 8 <%6  A6D -5: 7-?7? 95% λ - ?? %5' V0i =k,2λk =2(Ek + V0 ).`& λ 8 5&%6E E  A6D %), (@5: & ]#2!E#2#^E %' 5& %: %5 % 538aλ=+ 0.41 a (E + Φ),F3! G(E + Φ)?- 95%' 9?' 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(5: F!G -95%@ Ns.%<5E %:, 5&%' ) ?5: :&5, 758 556, 5%% 95%.95% %<5 W 78 9((% -&? 9'E :' ? -5 PBCjsCjCsCCjjCexp(−λT F |r − r |),W (r, r ) =|r − r |F#G?- λ P %% 9' .BE %' %-%: 7@) ')  - ?P`,%< 5' ' 95%, %%@: 5 5D'  sp.%55 8 56)%6' -56D K85LF H58 3GE %,E ?5 {ncE 5-% 58%6TFV0 = xV0A + (1 − x)V0B .#!4!+ $ ,:&5 (<D F""GE -5?' - 7%: %'@' ?56% 3vE %:, -?5 -%5 &5 )5@' 7?5 ?-E &%:' % 7) F">G ''% ]# "^E 8 )%6+++++c+k (t)ck (t)ck2 ck1 = ck (t)ck1 ck (t)ck2 − ck (t)ck2 ck (t)ck1 121212++c+k1 (t)ck2 (t)ck2 ck1 .F!GH-% , &% F!G F""G -%F#GA12 (k1k2k1 k2 ; E12) = AUP (E12) + ACP (E12),(−)∞(−)AUP (E12)=−∞∞ACP (E12) =−∞(−),dt −iE12 t + ++++ck (t)ck1 ck (t)ck2 − ck (t)ck2 ck (t)ck1 ,e12122πF4GF"Gdt −iE12 t +eck (t)c+k2 (t)ck2 ck1 .12πB)&, :5 %: A%6 F4G 5-DA -C(−)UP (E12 )∞(−)AUP (E12)=%%' '%:E 5 -%@+dE A(−) (k1k1 ; E12 − E)A(−)(k2k2 ; E)−∞−A(−)(k1k2 ; E12− E)A(−)(k2k1 ; E),,F>G?-A(−) (kk ; E) =∞−∞dt −iEt +eck (t)ck ,2πF/G#!"P -&%&' %56' (<' 7)E 5-% ) F>GE% A (E ) -&%&, %56, (< F#G -%5'@% 7, &% E 5D<D -&%&: %56: (<,5' :&5' 5- % 5& c (t)c E -'AD @%?5 , &% F/G 56)' %;' F">GE -(−)UP12+kk+++c+k (t)ck = uk uk αk (t)αk + uk vk αk (t)α−k + vk uk α−k (t)αk ++vk vk α−k (t)α−k+= uk uk eiEk t αk+ αk + vk vk e−iE−k t α−k α−k= δkk u2k eiEk t nk + vk2 e−iE−k t (1 − n−k ) ,?-F0GF2G%6 - &5 7?5 %' H-%5'' F0G F/G %?@' E 5& -&%&D %56D (<D 3vn u δ(E − E ) + (1 − n )v δ(E + E ) .A (kk ; E) = δF=G56)' 9%% )56%%E %5'% 7? %- :5%6 %?@ 9? 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