karlov-kirichenko-kvantovaya-mekhanika-2016 (810755), страница 23
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!# '! ( n = I1 /I0 = R1 R2 I0 e2αL ' F " ' "n > 1 ! " 226! "( 5;! !- '-M11.α > αc =lnAKKA 02LR1 R2< R1 = R2 ! " - ! AKKA "/ @! !2<1 5 !6!"#5 "1 0J5& '.! 0 -! 1 !" 0*& 0!& (' C " .'! ! '- !!& '"-( !5* - !6 !( '"-( 41* ! !5* **"! ( '! & " "#* ' ' 5* =! "( ( '& !! 1 '"-; - !65!"( !5 6 ( '"-( ! 4-# 5'5! '"-( 0 0 9 '!"!"#( 0!( ('# C " 1 !# 6 '"-.( " !41( 6 !& 0!& (' 5;!1 !# ' !"5* !# !# '"- ; ! ! ! " 5"5 "( '0( ! '.! '4! '!*41 "0( @"( & ! 6.
'"-( '41 !& '! "0( 5 ;& ! *!-5 "5 % !5 - !.65 0- !" "- ! 0' "' 0!4! *IO* ' !"(! * 0!!# "!"#( 0!( ('# .1 !"(( "5 '! '"- 6 6.( ! ( '"-(5 " ' 2"!# ! -! .! ! '& ! '"-( b"( '& !( *'"* 2' !!4! !" 0!& (' % 0.1 "- 0!& ('#4 /? 4! '& ! '"#!.! ."0 6 *! !( AKI %5Öåïü îáðàòíîé ñâÿçèÂõîäÂûõîä2 :0) = + 7 , = + ) @+"0D =A ;=< 0 1 0 ;?-< 5= + 0 4 1 0! 0!( ('# (" ( !* 0'-" #"!- '& ! ! & 6 " "!"( 6# ! % " ! !! ! !" (!# ( * '"* 3 * 0" 6" ! G'"-4! ! /?M ( <".!"#( /? ! "-4 !"( "404 ! 5.* " ! ! !5& '" 05 ! 0' 6 /?2"!6 !4! /!6!"#( /? ! #;4!"( 5* " 2"!6 '!*4! 9 0' ."!"#( /? 5"(! 264 - !5 !6!"#(/? 3 !0"'! !5 *'5 "'6 /? ! 05!#5 '"-5 ' ! ! ! !& ! !5% ; "- 5& 6 '"-( "'! ("!"#( 0!( ('# ! "1 3 !6!"#.( 0!( ('# <( ' * ! " 5"(! ( " " ! & n2 > n1 <! *! "'"-( % 0! "- 0" 1 !4 "# ! ."1 ! !6!"#( 0!( ('# '"- '!*!) !# '"-5* * -!( !5 '"!5 0- 1 ! "( & ' * "-!# "( .'0( /01 "( * ' * ("(! ( !0 ! -!05 " ' 22!5& * '"-( -' 4 ! .5;" ! '! ' !! *F " RK = 1 " "!5 ! 0" "! /.
"( '( !"0!"# 0* ! ,- .L- / 5)().L-.Z- B"(! (*(0" 2' G' " cos (4πL/λ) = 1 5"(! ( "( '"-.( !& - !!5 "( !& 2'5 0 ' 4! ( " '! "5! ( 6" - " "" =! "- !! ' "!"# ! 05!# "#' "( ."( - !!5 6% '"#!! "( - !!5 6 "# !"-41& ( ! 0"'.* 6!"#5* - !! " '! IB"1 I 8;8'5& 0 "' '! !! ' !* !"(41*/ ' * ! ('( "&5 ' '.! - !#4 ! ! !"# &- ! 7!"#5 - !! ' 5 2'5 0 0 ""5 . 5 & ! !"#& " "( "1( .0- 1 ! ' & & ( 0 ! '!"'% 1 ! -# ! '& 6 2'5* 0 .1* '!# * 5* "!* "' 3 0- 1 ! '!% * & "0!"#& 5 2'( *! ! "40. '! " !#4 "! !& "( - "0.!"# LCR.! 8'( *! ! - "0!"#.
! *; ' ! " '!# -! "5* ! !&*! ' & - !!5 "!"#5& 2'5 '! .!"(!ϕр = 2δωр /Δωр ,AKKI δωр = ωр −ω 3 ! !& - !!5 '"-( ω ! 6!"#& - !!5 !& '! ωр Δωр 3 ; " 5 ( '! & <!- "- ' 5! ( 2'5& 0 1 ! '.41& ! ! !& - !!5 '"-( ! 6! !.& " "1( =! !"# "# *(!( ! -5 ' * ( .!"# !; " !#4 0 " - - 6""(! (' ! < " "1( ;. #;! ( % 01& "5 ! #; "< 226! "( 1 ! G ; " "( !#Δωл / ln G Δωл 3 ; " "1( 9 "( "5* !.! Δωл = ωл − ω - !!5 '"-( ! 6!"#& - !!5 "' * ωл '5! ( -! 2'5& 0 1 ! .! 05!# !" ϕл = −δωлΔωлln G.AKKK9 ( ! 2'5 5 "- ".
0" 2' '41 - !! 6 "'ω=ωр Δωл / ln K + ωл ΔωрΔωл / ln K + ΔωрIAAKK ,√ K 3 226! "( "! ln K = ln G !! 6 "' !"-! ( ! - !!5 '.! ! ! - !!5 " " '! ! !- "4ωр = ωл ) 9"# " -# '& " " -# 5 ".( Δωл / ln K → 0 - !! 6 !! ( - !! " % .!" - ! "- -# ;& " Δωл Δωр ln K - !! 6 "(! ( - !!& !& '! =! .0( 4! ( !; 0" !5* !!- !!5 !5* ""(5* ! ?% ! . '.! & !5 "' !&- !!& '"-( 3 &8" AKK 05" "- ) <*5 AO .!"# - ' "# & ' 01'- 05" -! 1 ! ? !- '( 2' ".' -! "- ;& " - !! 6 "(! ( !&& '!"5 @ 2% ( "& "' '!# 0! !# '! Q "(.4 "( "0!"#& !5 !; Q = ωτE ω 3 - !!"0& !5 τE 3 ( ' ! ( 05! e ',"( *( Q "#'!# ( ! -! " '!*.E ! ! 0"( 2" Q = 2π 0 E0 3 (ΔE !5 -" ."0 "0& ΔE 3 ( !(.( ' !! G ! '! '5& AKA ,"("5 ! '! "0& T = λ/c ! ' ! 01( " *! !( " ".5 λ 2' "5 2 & !- (! ( Pπ D 6"" '! *! !# IL 5! ! ! * '." < ! !! ( ( ( E0 R1 R2 !(! ( ((ΔE)2L = E0 (1 − R1 R2 ) =! !( 1 !"(! ( ' ( * ".& ! IL ?!! ! ' T ! ! λ !( !!λ(ΔE)λ = (ΔE)2L ! -! 0! !# '! '5! ( &2LQ = 2πE0(ΔE)λ=L4πλ 1 − R1 R2.AKK,- .L- / 5)().L-.Z- B"(! (*(7 " L = 1 λ = 0,5 ν ≈ 0, 6 · 1015 >6 R1 = R2 == 0,95 ! 0! !# ! '! !! Q = 2,6 · 108 ,0! !# '! (' ;& ! '"-(M Q == ν/Δν ,"( ! '!,"( '! "& L = 1 м ( 0" !# !"(! 2λ21cΔλр ==∼ 1, 25 · 10−11 = 1,25 · 10−7 .AKKOIIΔν =νQ=0, 6 · 1015= 2, 3 · 106 >6.2,6 · 108AKK/- -! Δνν 9 0' ! "' '"-( ("(! ( 5 & ! *!- / ! ( ! ! 6 ;5 " '"-( '.! 05" ' 5; '! 1 ! "- .!2! 80 : < <! '"- ! !# ";#"5 "5 " "(5 !; 2L = mλ, m == 1, 2, .
. . =! '-( "5 "5 !-4! 6! "& .( '! =!! 5 ! "! ' 2"5AKIO !& (!# G = Gmax " cos (4πL/λ) = 1 9"#. ! "5 ! ! 6"!# '! "( *' "7& !( 0"&; " " !5 !';!# ( 1#4 '! < !# ( '"- "&"5 λ "!# ( ! ! '"- !& "& "5 λ -!(m+1)λ = 2L 9 ( 0" !# !2! "! ( " (m + 1)λ = mλ " λ − λ ≡ Δλр = λ /m ≈ λ/m "0" " " ( !26 m 1) 9 m = 2L/λ !Δλр ≈λ22L.AKKC " "( ; " '"-( Δλ #; - Δλр ΔλΔλр ! ' 5 & ! '! "0 '54! ( "(! (' 5 & ! & !"#& " % 0! "-Δλ Δλр '! 1 ! "(! - !! '"-(M .! ! '!# "# 0"'* -! *!- * "&< !# !! ' "" !5 A ∼ 10 ! M c2 ∼ 1010 эВ ,"( 6 "41 '-( !M !.! 5 KBB ≈ 1/40 % ! ! ( ' '0.
( "" τес ∼ 10−8 - !! '"-( ν ∼ 0,6 · 1015 >6 ""5 λ = c/ν ∼ 0, 5 9 ! !( ; " Δωес ∼∼ 108 с−1 " Δνес ∼ 0,17 · 108 >6 "#'( - ! 6 !( "" "- ( !"& ! υ ∼ kБ T /M & -! " ( ; " !"(!ΔνД ∼ νυc∼νkБ TM c2∼ 9,5 · 108 >6.AKKN2L2LIKν?('5& ! '0 - !! "(! ( ' ! "( -! νn =cc== n n = 1, 2, . . .
λn2L Δνр = Δcλ=с2L= 1,5 · 108 >6.AK B9 0' "( ; " Δν = Δνес ++ ΔνД ∼ 109 >6 "541( ( ' ! !& " & 0"#; & 0" ! ∼ 108 >6 '! "' 5"(! '-! *!- "?! ( "- Δνр "(! !"# !( ".( ! 6! 5* '! "& =22.!( ; & " "(( "; 26 ( G(λ) AKIO '5! ( #;M (Δνр )эф = ν/Q ,"(5 0! '! ! "- ! '!# ( 1 !#; - Δνр % ! '6 !"(! -! ( AKK<(!# '6 Δνр (Δνр )эф '"(! AKK !' ' !# G(λ) "( "-( K = 1 AKIO 7-!ν = c/λ ! -! Δν ν ! ( Δν = (c/λ2 )Δλ " Δν/ν = Δλ/λ?!! ! 2 ' 5* 5* G(λ) G(ν) .!- % -! 0"( 2 & G(λ) 22!(; " (Δλр )эф '5! ( #; - !( "( Δλр ?"!"# (Δνр )эф Δνр G(l)1(Dl p)ýôDl pl2 7 ,5 , G(λ) + =?7B - " )1 )" )4, 5)0 I,- .L- / 5)().L-..- ` + * / ( &" E 2! #! 6 ! "!"( *(1& 1 '! ' '0 "!"( < .'0( "(! ( ! ' "' "& 226! "( "!"( "' 2'5* !;& '0 '"(! &! - !! 6 +&( !( 0"#; 0 "! 6 ! 05!# & !"# * "&& !%5*4 1 !# "'5* ! "- "!"&"(4! 22! 51( "- ' 5* !# '"-( )5 0 !!# !! "#.0# .0 -!05 1!# "5& ! ! 15& !"6& !& "! /- ( ";# "41 .!5 0(8'- "'( 6( 0 "" '"- 5 .
& " !& ! !# 6 - -! ."(! ( "! !#4 " !& "(41& "-' - 0J !& 5 "' /6 !-! ! !# !( "41 0' < !# !6.5* "(* !# '( !"(! Λ - !6 -. 0J ' 6 9 "# '( 1 !#'"-( ! ( 6 0J ! 1 ! !"(!P = Λω.AK A=! ! !; ! 0" !- - 5; 1 !# "'! "- 5 Po2 ."' λ = 10,6 !& 6 -! * '0 ' ṁ (/ ) "#( 1 !# 6 !"(! 250 ṁ %! 5 *; ' "( '( 22! "( ".!!& "5 - " ! * !- ".
05!# 0"#; - < ' "' ( 0" !(" ' & " ! % (' ! ! 2." 4 4 ! '( ?& !& !"(! ( *( * !# !& "41 !65 5 0"4! ( !- !((. !5 *(! 5 *5 ( ". !# !& * '! ( 1#4 - 3 =! - 1 !!# 1#4 1 "!!'"-( < "0 '& ! *(! ( !( 0"' . 05-5 ( ' "( & Ni ∼ exp(−Ei /kT )! 0' '( " !& % '"#!! & !( 1"# - *(! 55 *5 ( & ! -! ! t = t1 ) " !# & '5.! ( !"& *& & " ! C " -0! "!# ( ! " ! & (4! ( !I=!! 22! 5 0 0 " 51& " / " .- 0! !!- "!"#& ! '"#!! & !( " 6.5* 6 "! "0& 0! #;!# ( "( AK N2−N1Δ N èí0t1tPΔΝ ðàâ2 (= + ) ,0 , D) )8 -U ΔNрав T + )D)-1 E ΔNин T )) ,B1) -E 5? 8 - ! !! ( !( 0"' '-( " !&N2 ≈ N1 9 0' "( "-( "# 22! - "05!# !& '-!# ( ! t = t1 ' !# " !& ΔN = N2 −N1 "# 75& "# - !05!# '1 !"# " -( " 65* 6 ' ' -! "( 22!& 0!5 ! *.& * 0* -!05 "# - " 0"#;4 .!"#4 ( !# ! ! - !!5 6 05" !!- !.5 " "!"# !# " 4 6""(6& " !& & ?" !# 1 !"( !& "# & .- ! !0"# !# '"-( 0 "" !'! !- ( *& *5% !(1 ( ; (4! ( !*( -!5*.( *5<5& "' !5& 9 )& 0!" AK ?!# !& *5 !! "41 < & !; !- *! 0 ! *& # QD! ' -! * *! ' " 0-( P % !& * ( " !# '! (.
R P *5 !5 '4! "' '"- !05! * 22! 0!" # Q " 05!# !!- ;. -!05 0 -!# 0"#;4 (! !# '*! F# P,- .L- / 5)().L-..- ` + * / ( &" 05!# {Z =! 0* "( ! -!05 -" 0.- * 6 5 '"-( '" !!-(' !# ' " !& & ΔN = N2 − N1 1 !"(4! ( U B Y ? !* & *(! 0'5'".-!"#5 *5 ' " 0- ( R'"- ** & ( R !( "* "5 λ1 = 694,3 нм λ2 = 692, 8 ! 0 *.!4 '4 ( U ! ! "& "5λ = 560 ( Y 3 λ = 410 ,"( - "' "#'.! ( ( " 41( ! ; !"# 'F U Y ("(4! ( ; 0 -4! '*! 10 ÷ 15 % .
"59*( * AK 0"! !! % - ! !1 -" 6 '!!!# 4 "( 5( '." !& ! '" ( P && ! !(( -! ( R +;# 5; ! "# '."( 0- ( -!5!# -" 6 ? !(' ! -! ' "'!# 54 64 '".-( 3 5& - !"! ( ! " ! ' " !# ( ! ! F' !! "; - !'( AK % !& * 0-& * 1 !"(! ( . ( Q P / " ! 0"#;& ;5 ( P 05 ! 4 Q !;! ( <! ( ". !# N3 > N2 *(! ( !- "40& ! '"(( Q =! '-! ' !# 5& 6 '"-(IE3Íàêà÷êàÇàñåëåíèå âåðõíåãî−3ðàáî÷åãî óðîâíÿ, τ∼ 10 c2Ðàáî÷èé ïåðåõîä−3τ∼ 10 c12 *0, 0) = + _ T ), 9 +, )4, ,) . 0G" !-( * & 0 "' ' AKG0- !" ("(! ( !"" 0 !(1& ' Uq2 o3 0& BB a Pn2 o3 5 !*"! * Pn 3+ '1.4! - !# "4( Uq3+ ("(! ( "!IEE4YÇàñåëåíèåâåðõíåãî ðàáî÷åãîóðîâíÿBR2R2R11Íàêà÷êà3UÐàáî÷èé ïåðåõîäÎñâîáîæäåíèåíèæíåãî ðàáî÷åãîóðîâíÿ2 ' H0, 0) + +02 $ :0) 0 , 0 ,=) + 7 =+-D0 , + =,B 08 Vvhw T ,= "? 0) , L =+ ,) U BB BY B , 0 =+0 , R = R1 B R2< -!5*& * 0!4! ! !!"#5 "'5 "' !" " >."' 1) hl3+ M UQ."' G0-;& '1& '& 5 * '4! "!"#5 .
'1& ' B R <*5 "1 !F==, 9F @ wnxA " ;9 3 F?)D <1),- .L- / 5)().L-..- ` + * / ( &!" !"(! 0& !"" ! ! - !# 3+'1 3 Uq5 o12 + 1,5a hl3+ / ( " "5'"-( ! "' !# λ = 1, 06 ?*( * "#'! ( '5* "'* % - ! ! '.5* "!'(5* "'* ( '! ( " '5* (* ( '0& "! '( & !- !& !5 6 * !".& 1* "5 26! '' ! (* "'5 ( !& '& % - ! ! AKN ' * & * "( "&. "' =!! "' 0!! 5. '! '"- " "5 λ = 0,63 %;& !- '0! !5 "( D! '"#!! !".& !5 "( 4! 4 '0( ! HY∗ ++ hY → hY∗ + HY + Eкин ( ! *(! 0-*5! ( ** "0!"#5 ( ""5?/2 ,"( - "' ' 0"(! ( '! !5& '0! ("!- '( '! ! 4 "" Po2 ! '4 # 0"(! ( "& !5& '"(! 22! 1 !"(!# !; "0!"# ( "" ?/2 9- !; 6!6& ! !"(! Po2 :h2 : HY = 1 : 1 : 8)5 0 0 !# !5* "'5* !6(* & !* "' =! *! ; '- 7 "# "5 !& "! ("(! ( ( " !& !.- & ! !5* & 5 ( 1 "# 0" !5* !*- * !.
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p : n.* 5. " "!5 !(( .!- * '< "5* !"" !& "!05" AOO " 7 > @ 5 AOK j "2.