Диссертация (1097858), страница 5

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, --E &%%E 7:5 )'% 8 %%@& 7% )< -95%: % )'8:&%< %% 5)? 5' 5, -& 9? @56 ]!>=E!/ ^ '- % )A, -5' %'' ; 5) 5 F#!#G 5&1⎡n|Ex p̂1,x − iEy p̂1,y |g1eiωtψT (r1 , t) = exp{−i[Eg t + ζ(t)]} ⎣ψg (r1) +2iωωng + ωn=gn|Ep̂+iEp̂|gx1,xy1,y−e−iωtψn (r1 ) ,ωng − ωF#!>G?- ω = E − E H56 ω ωE 8 56)%6 F#!>G )&@%% 758 ω ± ω ≈ ω 1% -% F ]!/!^GngngngngngiψT (r1, t) = exp{−i[Eg t + ζ(t)]} 1 + (Ex x1 sin ωt − Ey y1 cos ωt) ψg (r1).ωF#!/G5' (<' F#!/G %&% (5 % )A, -%5 % F{.-%5G 7- %8 %%%6E &%%' F#!/G -% - 57' 5)? 5' -&@ ;% -?ΔEg = ψT |i?-F#!0G∂|ψT ≈ Up ,∂tF#!2GP -%:, %<5 1% %&% )% (%E &% -5'%: % 5)? 5' |ΔE | U ):, -@%% 8 %%6E ?5E E 7% ]!/#^E  A6D 5-D@A, ): F#!/GC ζ(t) → ζ(t) − U t %  %E 5-% ) -@: 8 )56%%E %' )E -' (56 75 %D )@%6 -((<56? &' % 9?, &: 95%E -56 5'% ? )%6 % 56 %-& q E &%Up =E024ω 2gpp04 %% %'A? 5) -%5'% % q.)%6-((<56? &'56%%:, %7%:, -- 7:5 %%&7%E 'A: (e, 2e) <' % -- ]!/4E!/"^ ?5' ]!/>E!//^ %&, 5, % 5, -& 9? 56 %% 5)? 5' H-' F#!#G % -%5'% -%5D -5: a → exp[−iA(t)r /c]a Fl.-%5GE- )'A % )AD W (t) = E(t)r @'- %<, % )A, -5' 9%? 5&' -n1n1iψT (r1, t) = exp(−iEg t) exp − A(t)r1c⎡n|Ex x1 − iEy y1|g1× ⎣ψg (r1) −eiωt2ωng + ωn=g−iωt n|Ex x1 + iEy y1 |g+eψn (r1) .ωng − ωF#!=GiψT (r1, t) = exp(−iEg t) exp − A(t)r1c1(Ex x1 cos ωt + Ey y1 sin ωt) ψg (r1 ),× 1−ωclF## G56)' -5 %% (%E &% - &%% 8 -5Dω ω E %8 %% 758 FSRVZYUQ f[[UV…kXfTkVWGE 5&FE E ]!/0^Gng?- ω ω P K-''L &%% -<E 758 );? '- ;D ' F#! G @-%'  %'D ; %%% 5)? 5'clψT (r1, t) = exp(−iEg t)ψg (r1).F##!G1% 758E &%%E 7:5 56) A %%&5-' 95%.%: %5, 5) 5 FE @E ]!/2$!0 ^G0" -' +?- 5)' &%% 75) 5 -%  ω = E − E E -@DA, 5- %' F#!#G -D%  )78- %''; 7)E ; A%' -ψ (r , t) = ea (t)ψ (r ) + ea (t)ψ (r ),F###GfgT−iEg t1gg−iEf t1ffνfνg1ν?- &% )8 :8- )78-? %'' 9? 9(@(<%: )58' -'%' ; %: -((<56: @, F#!4G 5 a (t) = 0E 5 n = g, f H5- 8 -@5%6  A6D % ):? 758' ADA,' 5: Fdc PUVTfTkWg zfhQ f[[UV…kXfTkVWG ]!>^E % 7:% <55DA 5?:∝e ∝ e &%D%' 5: D  -5 <55@DA 5?: ∝ e )56%% 5&n±i(ωf g +ω)tν±iωt±i(ωf g −ω)t|Δ| + Ωiexp[−iζ(t)] exp − (Δ ∓ Ω)t ,=2Ω2√2Mfν ,gi±afν (t) = ∓ exp[−iζ(t)] exp (Δ ± Ω)t .2Ω(|Δ| + Ω)a±g (t)`-6Mfν ,g =F##4Gωf gfν |Ex x1 + iEy y1 |g2ωΩ = Δ2 + χ2f,gF##"GP %, ) FUQZVWfWSQ iQTYWkWgG 77A' &%% 7 %@%%E % ' Δ = ωf g − ω,χf,g = 2|Mfν ,g |2νP 7:&' &%% 7 `%E &% ?5 F##4G -5: 5-DA%;'C11|a (t)| +|a (t)| = 1,|a (t)| ≥ ,|a (t)| ≤ .F##>G22±g±fν2ν2±g±fν2ν20> 7)E %' ; 5& )? 5)? )5@&' %61ψT± (r1, t) = exp −i Eg t + (Δ ∓ Ω)t + ζ(t)2|Δ| + Ω2Mfν ,g×ψg (r1) ∓ e−iωtψfν (r1) .2Ω|Δ|+Ων5' (<' ; 95D<% ψ5 Δ < 0+T (r1 , t)F##/GE 5 Δ ≥ 0E ψ−T (r1 , t)E /##& $ )H5& :8' -5' -((<56: &, m€nO s€nO 5& -: :; -5, %'' ; %% 5)?5'E %: -5: (5 F#!/GE F## GE F##!G F##/G 5' 9%?56)' 5-DA %;' ]!0!^Ceiz sin ξ =∞Jl (z)eilξ ,l=−∞i−lJl (z) =ππdξeiz cos ξ cos(lξ),0?- J P (<' 35' <5? '- A6D -liexp − A(t)rcii= expEx x sin ωt exp − Ey y cos ωtωωππ ∞1 i(l+l)ωt −l= 2eidξ dξ cos(lξ) cos(lξ )π l,l =−∞00i× exp(Ex x cos ξ − Ey y cos ξ )ω2π ∞dξ1iLωt Lexp i Lξ − (Ex x cos ξ − Ey y sin ξ) .e i=2πωL=−∞0F##0G0/ !'  =>?H-%5'' (< F#0G F#!/G S .%< F#=GE 5&∞4iπS=−2πδ(Es + Ee − E0 − Eg + N ω)Fi,N (q),|p0 − ps |2F##2GN =−∞?- (<' Fi,N (q)%6∂∂e−iϕFi,N (q) = e+ iExJN (αq ) + JN −1(αq )Ey2ω∂qy∂qxeiϕ∂∂ψg (q).+JN +1(αq )Ey− iEx2ω∂qy∂qxiN ϕ`-6αq =Ex2 qx2 + Ey2 qy2ω2iϕ,eEy qy + iEx qx=,2222Ex qx + Ey qyψg (q) =F##=Gdr1e−iqr1 ψg (r1), 56 q -5 ?5 F#4G 5& %%%' 5)? 5' (@<' F##=G -%' F (q) = δ ψ (q) 5 ;6D '5'%' --@-7:, %  )'- '- Z Fg = 1sGE % ) F##=G 5&i,NN0 gZ 3 8πZ(q 2 + Z 2 − 4N ω) iN ϕFi,N (q) =e JN (αq )π(q 2 + Z 2)3Z 3 4Z(q 2 + Z 2 − 4N ω)= iNπ(q 2 + Z 2 )32π× dξ exp{i[N ξ − αq cos(ξ − ϕ)]},F#4 G0?- 56) % %; ]!0!^JN −1(z) + JN +1(z) =2NJN (z).z 7) F##2G 8 -%%6 & m€nO -∞d4 σd3 σ N=δ(Es + Ee − E0 − Eg + N ω),dEsdEe dΩsdΩedEs dΩsdΩeN =−∞F#4!G00?- s€nO F5 56:, (56GE %&DA, ?5AD FN < 0G 5D FN > 0G N (% %5DA,' %,E %6d3 σ Nps pe=dEsdΩs dΩe(2π)3p0dσdΩ|Fi,N (q)|2.eeF#4#G`-6 (dσ/dΩ) P %% & 95%.95%? '' F!>Gee !'  =@?-H-%5'' %' ; F## G F#=GE 8 -%%6 m€nO ∞d4 σd3 σ N=δ(Es + Ee + Up − E0 − Eg + N ω),dEs dEedΩsdΩedEsdΩs dΩeF#44GN =−∞?- U P -%:, %<5 F#!2G 56:, (56 F#44G% %D 8 (E F#4#GE ?-E -E F  F##=GGp2πdξexp{i[N ξ − αq cos(ξ − ϕ) − β sin(2ξ)]}2π0i∂∂Ex sin ξ× 1++ Ey cos ξωcl∂qx∂q yExEy×ψg q + ex cos ξ − ey sin ξ ,ωωFi,N (q) = iN?-Ex2 − Ey2β=.8ω 3 5& ---7? %  )'- '- Z -F#4"GF#4>G2π4Z exp{i[N ξ − αq cos(ξ − ϕ) − β sin(2ξ)]}[q 2 + Z 2 + 2Up − 2αq ω sin(ξ − ϕ) + 4βω cos(2ξ)]30ω× q 2 + Z 2 + 2Up − 2αq ω sin(ξ − ϕ) + 2i cos(ξ − ϕ)ωclω+4βω cos(2ξ) − 4i sin(2ξ) .ωclFi,N (q) = iNZ3πdξF#4/G02H% %%? 758' )-6 8 <%6 ω ∼ Z /2 H@56 ω ω E ?- ω = E − E = 3Z /8E 5?: <56:%;D ω/ω '% 5;6 5: F (q)cl21212p221scli,N !'  =?1%% 5&, %5&%' % -:-A? :8 -5' 56?(5'2πFi,N (q) = iN ψg (q)0dξexp{i[N ξ − αq cos(ξ − ϕ) + β sin(2ξ)]}.2πF#40G56)' F#40G 5&E ?- ;6D '5'%' ---7:, )'- '- : Z E 5&Fi,N (q) = iN4ZZ3π (q 2 + Z 2 )22πdξ exp{i[N ξ − αq cos(ξ − ϕ) + β sin(2ξ)]}.F#42G05 5) 5 <5' 5')E %E ?5 F#4>GE β = 0 E5-%56E 56:, (56 F#42G % - F  F#4 GGFi,N (q) =Z38πZeiN ϕ JN (αq ).222π (q + Z )F#4=G " !'  =>?56)' F##/G S .%< F#=GE -5' m€nO 5&∞±d4 σ ±d3 σ NΔ Ω=δ Es + Ee − E0 − Eg − ± + N ω ,dEsdEe dΩsdΩedEs dΩsdΩe22F#" GN =−∞?- 56:, (56 %6±d3 σ Nps pe=dEsdΩs dΩe(2π)3p0dσdΩ±|Fi,N(q)|2.eeF#"!G0=`-6±Fi,N(q) = eiN ϕ|Δ| + Ω2Ω 2Mf ,gνψfν (q) .× JN (αq ) ψg (q) ∓ eiϕ JN +1(αq )|Δ|+ΩνF#"#G5' ---7? %  )'- Z |f ≡ |2p Fm = 0, ±1G E?5 F#"#GE -νm|Δ|+ΩZ 3 8πZ±iN ϕFi,N (q) = e2Ωπ (q 2 + Z 2 )2 5222 22αq ω (q + Z )2× JN (αq ) ∓JN +1(αq ) ,3 |Δ| + Ω (q 2 + Z42 )3F#"4G?- 77A' &%% 7 Ω= 5 2 28 ω21 E0Δ2 +.9ω2 Z 2 !* 9% )-5 -%5: 5): )56%%: &5:&% -((<56: &, s€nO -5' (e, 2e) < % -@- FZ = 1E E = −0.5 fYG %% 5)? 5' %'% %' 8E )-5 !"C θ = θ = 45 E E = 2 keV − E E = E = E F  !!G & s€nO 5-%' (<' 56q E %:, 6%' -% )' )%56? ?5 A@? 95% φ ( )%56 ?5 '? 95%φ H 9% -5' :7? -) )&, q 9((%: 8' 5@ 5 %? 7? 758' %%% 5)? 5' ?D% )%, 5 %, % F )-5: !" !/G 7)E 9% 9((% 8 7&6 5& %%'5)? 5'gsseese◦0g2 5& 5,, 5')< Fle P RkWQfU [VRfUkfTkVWG %D%@' 5-DA %< 95%&, %: 5)? 5'C E pFle!G E ζ Fle#GE ?- ζ = [p × p ] 5& ?, 5')< FneP SkUSYRfU [VRfUkfTkVWG 5-D%' 5-DA %< 5? %5)? 5'C k ζ Fne!G k p Fne#G %&DA' 8 -%:%: % q %%' % -%E )-, 5: @5')<: % 5)? 5'E %: -5: )-5 #!00s0" 7!' +:7 %: 5)? 5' % 8E 5& oiCŠcp5)E 56)?  (e, 2e) 9% %% 5@)? 5' ]!4^C (%' 9?' ω = 1.17 9E %%6 I =4 × 10 %a 7)E 5)' &%% ? 6;E & &%%1s → 2p - % -- ω = 10.2 Q{E 5%- 95%&@? 5' E ≈ 10 fY ? 6; %? %%? 5'E ∼ 1 fY_5: &%: 7:5 :5:  %' %7%: -5'@ %'' % -- 5) 5E %: -5: (5@ F#!/GE F## G F##!G %%% `%E &% -5' -? &5 (%@E %: 7D%' %5DA'' % 5) 5E 5&@ 9? &? 95% E -5 F#!/G ):%' 5@ -%? %<5 F#!2G 756;E & 5& -5, F## G F##!G 5' 78-: )&, 5): % 9% )< %@5'% 5 0.21 9 56 )& 56 qE % 5)%' 5, % Fφ = 0GE ):%' -5 F#!/G %8%5&: % 5&' -5, F## G F##!G -E )< 8- 56@: )&' q :;% 2.5 × 10 fY -5' N ≤ 2E &% -%'-5 ) -5 56? );' : 1 9@%E E 5-%56E ?% 5 %% %'A? 5)122210−2He−32!  #!.#" -%5: )56%%: &5: &% &, s€nOE%&DA )5&: 5&' 5')< %< 5)? 5'E-5: :;E %8 )5&  &5 (%E ?5@A:aA: %5DA,' %, F95% ‰ % --G5& s€nO 56 N = 0 )% -%  % @? &5 (%E )-,%: < ' %-<' -5 %56 -5' |N | ≤ 2E %8 -5' <  |N | > 2E %: -@%5:  #!.#" 1% - s€nO )% % N 7b''%'57, %%6D ),E ), &%%, 5)? )5&'P '%%6 ?(%: < ) -%  % &5 &%@DA (e, 2e) %5 (%56: (5  #! #4 N = 0  % @-5, %'' % -- 75) ( 5& 56(5D 5& 7) 5)? 5' E &% 5-,  %&%6D -%&? (% -5'%' 56: -5 95%@ 1s %' % -- |ψ (q)| E % ' : 758-5'D%' 5&, |J (α )ψ (q)| ?% (< 35' 5?'- %' F le! ?%G 5 &% %' F ne! ?%GE ? 5& %6 α ≈ 0.2 fYE E 5-%56E J (α ) ≈ 1 ]!0!^ %5& %  #! #4 56: (5 N = 0E ):  ## #"E &% %5&D%' % )56%% 5& 7) 5)@? 5' 1% )< 755 (<, 35' J (α )E &, ?%758 α ≈ 5.4 · q le# ?% α ≈ 3.8 · q ne# ?@% 5-%56E %5& % 5& le! ne! )'%' ;@ -) )&, 6 )%56? ?5 A@? 95% φ 75D-: <55'< 56: (5,  ## #" 8 7b'%6 - (<, 35' J (α ) ,%%56E)5: 56: (5, -D%  )5 (<, 35' H56J (α ) = (−1) J (α ) ]!0!^E %: <55'<, -5' N −N 8 @21s0qq1s20qq0qqeN−NqNNqq2# -./0 12 q $ N5 @ N = 0 >(% % % 1 $ $ >4$ $ , ) "+! ' , ) E+! >4D ' , ) +24 L 3! ! $ N5 2" = L 3! ! $ /5 2> B L 3! ! $ /5 2/? %5& % 5& le! ne! )5D&%' %E &% 5& s€nO le# ne# ?%' -5 7:%  % ? &5 &%@DA < (% &%: ):D%E &% 9% %5& '%'%8 |N | > 2H5) )%6 56: (5, % %'' %-- 5) 5  % 78-: -5 -D% - %% 8'- -5' 5&: s€nOE ) 5D& 5&' le! ?%E ?-N = ±2 F  #!G ,%%56E 9% &% 5& & s€nO -5 F#!/G - '- 6; 5& D 5&' -5, F## G F##!G 1% )5& 8 7b'%6 56D @% β ] F#4>G^ :8' F#4/G F#42GE %:, %%%% :8@ F#4 G 35 %?E ne! ?% F #4GE %' ) %:75 ()& 75) le! ?%E %, 6), )<: 8--5' N = ±2 75D-%'E % 9% 5& β = 0 5-% ) )56%%E -%5:  #!.#"E 5& @-5, F#!/G F## G <:  ?5A (% FN < 0G 75 '%:E&   FN > 0G : 5E %5DA'' % %%@' 5&%6 9?D % 5)? 5' -E 5& -5 F##!GE % &%:% )-,% 5)? 5'  ;6DE <: '(% - 5 -8 75 '%:E & <: ?5A' 1%):% %E &% ?5AD 9? 5)? )5&' %5@DA,' % %%' D &-6 % --E %:,  )A %' -5D 8% %6 (%@: F %5& % 7-: 95%G8 -5%6 7A 75D-E &% 56: (5 -%%&&%%56: %7%, -5 %'' % -- 5)5 -E 9% &%%56%6 )% % &5 (% E N = 0 )56%%: -5, F#!/G F##!G %& )5&:E7 5&' ne! ne# 1% ')  %E &% :8' F#4 G F#4=G20-%&: N = 0 _%%56%6 %8 )% % 5')< 5)@? 5' E 8- )56%% -5' 5& %', F#!/G F## G 75 :8 5,, 5')< 5)? 5'E % le! le# ?%'" -' + - 5& 5)' &%% 5 75) &%% 1s → 2p @- % -- 5%- 95%&, %: 5)? 5':7 , E = 10 fY H-5?%'E &% -5%56%6 5)? @56 T Γ E ?- Γ P ; 2p 'E 755' %, 9@, (%)<, 1% %7 ?%%E &% )5% 1s 2p @%', -5'D%' ; F##4G 5' :7, 5&: 5)? @5' 5& 5 T 10  % 8 'E 5& T -58 7:%6 756@;, ;%7 %, , ;5: F∼ 10 G ? :;%6% ' 95%.95%? %5, F∼ 10 − 10 G? 8 ?& )5D&%' %7E &%7: ' 5D&@' :5D&' 5)? 56 δT 7:5 ? 756;E & ' 7@- -5' (' %'' % -- ) 5)5 F##/G 5& 5-? 8 ?7 <%6E 56)' &%% @7E 1/χ 5& E = 10 fY χ 7.45 × 10 fY E 5-@%56E δT 10   #>.#2 -%5: )56%%: &5: &% -5' 56@: (5,E %&DA ): ?%' )&' -, @%, ) η = Δ/χ )56%%: ): %56 -5' 5&7) ?5A'a' (% FN = 0G -(%? ?5A'FN = −1G -? 5&' FN = 0, −1G 75D%: 5&: 56:(5, '- 6;E 5 5, %% 5)? 5' )? % ?(%: < : 5E 9((@%: )-,%' 7-: 95%  5): 5E % &%:@−40−1−10−17−172p,1s0−4−132p,1s2p,1s−5−1622L2 M % 1s 2p %! |a1s |2 O68 ) =+ 12% $&% % ηη|a1s |2|a2p |2 !$ 3|a2p |2>>> 0#4/ #0/"! 2>4/ !"/"%' -% 5 %', F#0GE ):D%' A%:E -5'DAD 56 ?% ) )-,% % -- 5): 58 )%%6E &% )56%%: -5' N = 0 %& &%%56: :7 ?% H& 9%? %' ,% :8' F#"4G 5'78-? :7 % 5)? 5' )& ?% (<35' (5 F#"4G %5'% α < 10 7)E 8 56@)%6 5-DA 758: :8' ]!0!^Cq1 αq NJN ≥0(αq ) =,N! 2−3(−1)|N | αq |N |JN <0(αq ) =.|N |!2?5 9% <E N = 0 5- 5??E -8A? J (α )E (5 F#"4G ):%' 56 -5: 5-%56E 56:,(56 5%6D -5'%' F %&%6D - %&? (%G5&, |a | |ψ (q)| E ?- )5%6 1s %'' |a | F %75< #!G )% % ?% %5& % 5&' N = 0 )56%%: -5' N = −1 56 )'% %:7 ?% 5)E 5?&:, - :; -5' N = 0E @):%E &% 56:, (56 -5' N = −1 -5'%' F %&%6D- %&? (%G 5&, |a | |ψ (q)| `5%6 2p %@'' |a | F %75< #!G )% % :7 ?% -E 56@ -5 95% 2p 7%5 |ψ (q)| E  %, -%11s21s21s2p2p22p222p22q2= F -./0 12 q $ N5 @ N = 0 >(% % % 1 $ $ >4$ $ , η = 0! ' η = 0.5! >4D( ' η = 1= " L 3! F! $ N5 =! 9 L 3! F! $ /5 =#  L 3! F! $ /5 =4)<'E )% % 9%? :7 7:& 1 9% %';6 '5'%' 5'), 1% )&%E &% )'%' 56:,(56E %:, (& - 5' 56 q FE @E ]! ^G % 5&E -E 5) 5 5')%;6 5 56 q &% ?%6 56 ?5 F##4GE @5') 2p %' -%5'% 7, 6 2p 2p %', 5& le ?% 8πq|ψ (q)| =,F#""G(q + )% 5%%6 56? -5' 56 F 5DGE ?-q 555 F-5'G % 5')< 5)? 5' le!?% F #>G )& q '%' 56 )&Dq Fq= 0.01 fYG 7)E ( 56? (5' -5' N = −1)% %56 % )%5' (5 F#""G le# ?% F #/G75D% )& q '%' ; -)E &'  5' 1%7b''%E & 9% 5& 56: (5 -5' N = −1 '-@ 756; 5& D% -?D ( D  5& le!?% 35 %?E ) %%'  5& le!E 56: @(5 5& le# )% 756; 5& -5' N = −1E & -5' N = 01% ):% 75- le# ?% 1.<  &% @5')? 2p %'' % 1s %'' &%%E 56'5& 56? (5' -5' N = −1 ):%' '- 756;E& -5' N = 0E ?- 5)%' 5 %&? ) Fη = 0G E ?5%75< #!E 1s 2p %'' )5: - 1%% )56%% -%' %%%  ; )%: (%E &% 95% 2p %' 57') ? 5?& :7%6 D  5& 1s %'' 5& ne?% 4π(q + q )|ψ (q)| =.F#">G(q + )%D- 5-%E &%  5%% 56? -5' 58% +1LP2p2x1 6422xminxCP2p2x222y1 64−1="5% -5', 5 % 5)? 5' k 5& ne! ne# ?% 7:%6 5): 5?  5&' le! le# 3)% 7A% 8 &%%6E &% 6 x 5556 56 p ?-E ne! ?% F #0G )& q % 8E 5& le! Fq =0.01 fYGE )& q )'%' % 5' F?- q = 0G - 75)%56 2 fY F?- q = 1 fYG 7)E ) ' :8, F#""G F#">G 5-%E &% q ∼ 0 56:, (56 -5' N = −1 5& ne! - ) 6; 5&E & 5& le!E % ' 7‡56;)&' q  5 -8 -% 5& %%%DA,56:, (56 le! ?% ne# ?% F #2G )& q)'%' % 8 -)E &% 5& le#E 75D% )& q q q /(2√E) ≈ 0.08 · q 5 9%? 5& %: q ?%)&%56D 56 :8 F#">GE 56:, (56 -5' N = −1 5& ne# %6 % %%%DA, 56:, (56 5& le#E8:, (% !a#`%6 56? (5' % 5&: -, %,) η 8 -% 7b'%6E -' ) )58? :;5) %75<: #! ,%%56E 5& %&? ) Fη = 0G5& 56? (5' -5' N = 0 56E -5' N = −1 @56 % F6;G η 5& 56? (5' -5' N = 0%% F6;%'G % 8 7)E 9% -%  1s )5%6D|a | E %?- 5& 56? (5' -5' N = −1 6;%' F@%%G % 8 7)E 9% -%  2p )5%6D |a | = 1−|a | `% 9%, ')E &%E ?5 F##>GE |a | = |a | = 0.5E 5 η = 0E |a | > 0.5E |a | < 0.5E 5 η = 0 A - )& %% %E &% -5' &6 756; )&, |η| 5& η −η %& )5&: 1%')  5%6D 77A, &%%: 7E %'E % 7)E &657 5'% )& 9? &? 95% E E %8  78-@;,' :; 5%6D % α E %' -% %E &% 5?:E0xxyxyy1s2x2xy22p1s1s22p2q22p221s2=>:DA %(<D 1s 2p 5- F∝ J (α )J (α )G &s€nOE ):D%' 78 5: )5D& 5) )? 5&' 7- -5%6 56)&, %%56 )8, 5)< 1.), %%5)? 5' %'A, % % -%: 5)E 7%DA &%% 1s → 2p - % -- H9% 75 --'A--% 56 ;  9%, %& )' ?5 7: 58%6 A5&@: %: 5 : E % 5%' %' 9?' - )? )78- %' ? 6;E & --E&% )5'% 5)%6 5' )  DA' 5) &-@E &% -5' % 75 58: D  -- %: %5-% 8-%6 &% 8 )56%%:NqN +1q' ! H-:, -:-A )-5 5) 'A 5-D %@?E 5' 5)? 5' %' ; %8%' &'s€nO - )-5 %%'  &%%56% &,s€nO 8D 5 5 5) 5 E &% 9%% 9(@(% &%:%'  A6D 5 (<, F#0G 7:5 %@5 -:-A )-5 % --E ) 8@ 9((%: 5 (<, ?D% )&%56D 56E % 8&6 57? 5)? 5' FE ∼ 10 fYG ):%' -%%& -5' 9(@(%? )5' ? )78-? %'' ; 7%' 5&D )&%%? 8 %%%DA % 5)@? 5'E 78-;' -:-A )-5 :, )?5'-E 5'5)? 5' 7:%: 95%:  9?' 1 − 2 9 -58 ?%6%%D 56 %- 1E 5 &%% F∼ 1 /G %%6F∼ 10 − 10 %a G 5)? 5' )% 5: %: ;%7 012132−4=/ E 8 )E &% 9% 9((%: ?% ?%6 8D 56 1< % %% 5)? 5'_%7: 55D%%6 56 78-: 9((%E  )56@%%: &% &, -5' 5&' % --  5 (<'@ F#0G 5 5 F#2G :7 -5' -5% &%%'' ; 5) 5 758 F#!/G :8' -5' 9@5D): &, m€nO s€nO 5& :7? %'' ; 5 (<, 7:5 5&: )-5 #4 F (5: F##2G.F#4#GG 5& 5 5 F#2G -5' &' m€nO ∞d4 σd3 σ N=δ(Es + Ee − E0 − E1s − Up + N ω),dEs dEedΩs dΩedEs dΩsdΩeF#"/GN =−∞?- & s€nO F56:, (56G -5' % -- -%' :8@ F#4#GE % F  F#4 GG√8 πF (q) =J (β),F#"0G(1 + q )5 N &%E √16 πωαF (q) =[J (β) − J (β)],F#"2G(1 + q )5 N &%  #= #! -%5  &5: )56%%E 5&@:  5 5 5 (<'E -5' % 5)?5'E % 5& 5,, 5')< Fle! le#G % 8E 5) )&%%? 8 )-5 #" 5' -7% ')56%%: -5' N = ±1 5& 5 5 7:5 8: 9((<@% :, ! )56%%: &%  5 (<' 78-56 -:-A )-5 F  #! ##GE 9% 8 %' 75-7 ,% 56: (5, 5& 5 556:, (56 -5' N = 0  #= 5& 5 5 F#2GE%8 5& 5 (<, F#0GE 75) ( 5&i,Ni,N2 2 Nq2 3N +12N −12=0TDCS ( 10-3 a.u.)4Field-freePlane wavesVolkov wavesN=0321000.20.40.60.81q (a.u.)Plane waves (x10)Volkov wavesTDCS ( 10-5 a.u.)4N=1321000.20.40.60.81q (a.u.)6Plane waves (x10)Volkov wavesN = -1TDCS ( 10-5 a.u.)54321000.20.40.60.81q (a.u.) ; -./0 12 q $ N5 @ N = 0 >%% % 1 $ $ ' $ ) +! >4$ ' $$ 12 ) 9+=2TDCS ( 10-3 a.u.)4.0Field-freePlane wavesVolkov wavesN=03.02.01.00.000.20.40.60.81q (a.u.)0.8Plane waves (x10)Volkov wavesTDCS ( 10-3 a.u.)N=10.60.40.2000.20.40.60.81q (a.u.)1.2Plane waves (x10)Volkov wavesTDCS ( 10-3 a.u.)1N = -10.80.60.40.2000.20.40.60.81q (a.u.) E L 3! ;! $ N5 == )56%% 5& %%%' 5)? 5' E &% 5-, F%&%6D - %&? (%G -5'%' 5%%6D 56@? -5' |ψ (q)| E % ' 5& 5 (<, @5&, |J (α )ψ (q)| F?5 F#4 GG 5-% ) F#"0GE 5& 5@ 5 56:, (56 -5'%' 5&, |J (β)ψ (q)| le!?% ?% (< 35' J (α ) %' 758 α ≈ 0.2 `& ?% (< 35' J (β) )% % q -5'%: % 5)? 5' %6 β ≈ 0.18 5-%56E J (α ) ≈ 1 J (β) ≈ 1 ]!0!^ -E 5&' N = ±1 %<' &@% ' P )56%%:  5 (<' :;D% '- %% )56%%:  5 5 H& %? 8-@' %' )% :8, -5' 56: (5, F#4 G F#"2G%%% %5& %  #=E 56:, (56 -5' N = 0 5& 5@ 5  #! &% %5&%' % 56? (5' %%% 5)? 5' 7:5 %& )-5 #"E 9% ')  @- (< 35' J (α )E &, ?% '%' ; -))&, 6 56 q le# ?% <55'< 8 @56: (5,E 75D-:  #! 5& 5 (<,E'):  <55'<' (<, 35' J (α ) H  )&' N E -@%5:  #! E )56%%: &%  5 5 )%56%5&D%' % )56%% 5& 5 (<, %56 5@&E ( H5- 75D- 7 8E 56 19%: % 7:& -'%' )56, ;5 %@%, E 5-%56E 5-D% %56 ( 56: (5,?5 F#"0GE )56%%: -5' N = 0 5& 5 5 -D% le! le# ?%' 5-% ) F#"2GE le# ?% - @56: (5, -5' N = ±1 5& 5 5 -5'%' ?5:7) q.)%6D % α F7 5: )&' qGE @21s0q21s00qq00q00qNqq1s2!%' 78-56 -:-A )-5 7) -%5: 9%E %8 -:-A )-5 &5:)56%% 8 -5%6 5-DA :-: 56: (5 @%% 5)? 5' 56 )'% % 5' 5')< 5)@? 5' 8 756; )&' &%%: Fω ∼ 0.1 fYG 5%-:5' FE ∼ 10 fYG &% 5'' 5)? 5' 5%DA, 5%DA,95%:E 56)' 5 ;' F#0GE 6): 7) '% @5& ( 56: (5, ?5 - 5)E 565 (<, -5'%' % α = |E q|/ω H 9%E @?- α 1E 9((%: 5 (<, K:D%L `% 9%, ')E&% -5 % α (?% A - ()&, %x = E /ω P 5%- 5& <55'<, 7-? 95% 5@) 5 F#!G 7)E 75% )&, 56 q 1/x 9(@(% 5 (<, 8 7&6H56 75 ()& %: )&' q 7:& 58% %5 % 5' - 56 %: -<E 8 5 5 5) 5 7-% )&%56:  9% -) :55' x 1 fY E &%% 8 ω ∼ 0.1 fY ) 9%? 5'-E &% E 10 fY H %56 57: 5'E -E 5' 5)?5' %' % &6 5E 5 %56 5)' &%% -%@' )  &%%, - % ) 8 -8 &657 5) 5 8% 9((% )5'%6 )78- %' % 7)E '5'%' 56' )8%6 'D 5@-%6 56 -5 95% )78- %'E %' 7:& F7) 5)? 5'G 5-D%' 56: -5'-5' ? %'' ) 8 8 )%6 9(@(%: 5 (<, 5 5-' 56: (5, ?% E ⊥ q -%% -, ?% )5D&%' %E &% ,56 -5 95% ; 5-%' %56 5@−20q02qq0020000−3!! -5' E E % ' 9((% 5)? 5' %'% 5 5 5556 E ' :;)E%- 1 8% 7:%6 75 9((% )& 56: @-5, %: 95% 5) 5E 5 5) ):,8E %%6 5)? 5' %E &% α 100q!# " " " ' ?5 'A <E % 95%  5: @% F56G k 9?, E 77-% %6 %-%56,;E )56%% &? ) :5%D% - 95%  5: %@ k E k 9?' E E E F  4!G -:-A ?5E )-6 -5 8, - s (e) 7)&% ':, FA:,G 95% 9? )'D%' %%56 ? 'E % &% '-' %60s0esekj =2Ej(j = 0, s, e).

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