karlov-kirichenko-kvantovaya-mekhanika-2016 (810755), страница 2
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! 5 0( !"(! ( ! - !!& ν = ω/2π "& 6 "-& hν =!! ! !& 6." ! ( "! "! ! '& !( ! 9 "( - !# ( AK 3 ! hν ! (."(41 ( ! ' #4 ' *( !"! ! 0!! AN122mυmax= αω − β.K ?1 !! ""( " ( 6 2!22! =!'-! -! 2!22! 0"4! ( "* " ! λ > λ max ," "5 λ max !# *! ! 1 ! ' ! ! - !!5 ! ! ! ' *+ ,+ - 8!22! ("(! ( !- 0'565 *+ ,+ - D41 ( "& ' ! ! - !!5 !MVз = aω − ϕ,- !! a ' ! ! & ! 0"- 1 ! 0+ !C " 5& ' 1 *!( 05 - ! 0J( !# . " - * !"& '& ! ! "! ! !"#5 '5 !"5 !"# - ! "-.! *(! ( 41 !- "5 55 !" !% " " - & !- '( & ! "!.!& "5 - !!& ω "! ;! "0( !& - !!&ω "!& 6"#& "! "5M x ∼ E(t) ?!.! ! !- ( ( "! ! ( 6"#&! ! '"-(M Wкин ∼ E 2 или Wкин = αI <! 5"!"! ' 1 ! ! ( '5 " "- Wкин 5.;! 0! 5*M2mυmax2= Wкин − Aвых = αI − Aвых .9 0' " - ! ! 3 !- ! 3 5 -! !# 2!"! ' ! !! ! '"-(' (#)#! ! & % !" ! "#0! =&;!& " ! 2.!22! !5 !"( " -! 5& ! !! ' ' 3 ! 7 " ( !5* !05" 5 ' ) <" ' "# "! ! "( 0J( (12W = mυmax+ Aвых = eV + eVвых = hν,2AOA " -122mυmax= hν − Aвых .A% ' !" ! <!5 II K 0J( (4! ( ( A '( '54! !- !! ! !( 0"45 5! ' !( ,"( '5* !""' !# "#& !- & 2!"! ! -.!!5 ! !! " AK =!! " ! '- !(& <"M h = 6,63 · 10−27 эрг · с = 6, 63 · 10−34 Дж/Гц ( 6 2!22! 3 hν0 3 ! '- 0!5 5*Aвых F 1"-5* !"" !5 " !4! & ;& "! ( 6 2!22! "! '" ! ,"( 0"#; !* !"" ! "#!2"!76 ' )"" " "! ' 2"5 =&;!&.
A " '!!# -! "- eVз !# !- ! "#(,- .- / )(! IB.-9- :++ ;!- ( ( 2!"! 9 5( A Vз =2mυmax2ehAвыхee= ν−≡ aν − ϕ,A"- !- ! ' D! -! ! !; '"." 1 !!# ' !(& <" " 5* Vз (ν)mv 22(1)ν0ν0(2)ν2 /) )) - 1 D - ,0 )B -?80 = 0 Aвых! 2!22! ! 5 !& ! >.( 0" ! ' ! 2!22! (! 5 !.& '& !( ! 1 ! 7 !# -!( !5* ! -# " ,"( "! ! "& "5◦λ = 6000 U = 0,6 !! ! - !!& ν = ω/2π = 5 · 1014 >6( ! hν = 3,3 · 10−12 ,"( !* ! * "-&◦λ = 1 U ν = 3 · 1018 >6 ( ! hν = 2 · 10−8 % ! ! !! !& (( ( !" .( !* ! -# " %"- kT !!'-( 3,3 · 10−12 T = 1, 6 · 104 '-( 2 · 10−8 3 T = 108 =! 6 0J( (4! - !"# !(!! !"" '5! ( 2!22!/6 !# - " ! ! 5* 6 ! 5 !- 5& 2 C " (!# -!"!5& ! 1 !#4 A %! 1! "1# 2 ! "&! -! 5& !5& !! ! (! "-! 6·1017 ! 7 !( AB * !! - !" 5 " BA !! 2 '! 1 !# 3 · 108 ! 2 IA)5 0 !"!# ( !* * !& 2!.22! "* "-5 0! 2!!" .
( 2!22! /0 ! - !# > ? + 0 /! !( ! (* +<"& ( ! !# ! (" # 5!* 5."5* %"#! @! AOI ?* 5! ' A % !* 5!* ! '"-R-# "& ! ! " !4 !""- 4 2"# !( 4 -# !" # !- !.- ! '"-( ! '." ! ( 2" 66( "&C1C2! ! =! !- '"-Ô !" # ( -!- ."5 '5 !5 ! 2"#?"5 ! -!- !" "!.Ë!5 5 '( ! !5*' 5" # "!C " 05 ! !"(" 0& "Ý1Ý2! '"- *" 05 0* -!.- ;!* "! "" # 05 !- % & !.!"# ! "5 -!- !" M ;!* "& .
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
"( 41& "5 "! 0! ;!# "0( ' 226! λ0 = 0,0242 U ! '- - !!5 θ = 90◦ IImr̈ = eEпад (t),−iω tEпад (t) = E(0).пад e(0)r(t) =eE− падe−iω tω2=−eEпад (t)ω2.9 0' "#5& ! "! d = er - (.! ( !! ! ' " - & "! '!"# '"- ( ! "!- ! "&! "#& ' '54! ( 5Eизл =Hизл =1c2 r[[d̈n]n] =1c2 r[d̈n] =e2e2c2 rc2 r[[Eпад n]n],[Eпад n].D # n = r/r 3 -5& ! "5& ! "( !-0"4( ' !* 2" 5 ' ! 41& (& " 5MEпад ∼ exp(−iω t),Eизл ∼ exp(−iω t).7 5! '" # -! !"# (4 ! *"-& " - ( !( ; !(!"#?* 5! 22! ! ' AD # 25 (4! ( "( ! -!05 '!# '& - * '"-( -! 0* "( "5* '& ! * '"- *!'! ( -! 0* "( !"#.5* '&% ( ! ( '"- *& " "5 λ05" 0 '"- & " "5 λ 3 A <! '" # -! "- Δλ = λ − λ ' ! ! '-( λ ! !" 41 !" ' ! 05" !"' !# ! " ((MΔλ = λ0 (1 − cos θ),◦Ä 1 Ä2IÐ.
Â.θϕÊð.lÈ. Ê./! 4 "! -!AIK2 :0) () %=+- 0)U 1 B 2 T 1) ,+D1 ,- )0)-1 +,-E 2 7 T?8 8E ( T E 9 ( T+5 )l2 $ : 1D1 +,-B D1 1) 8)/'" # ! -! - !(" 1 ! ! "0 ! !#1& " ,"( "* 1 ! VW XY X !- ( '"- ! 14 " "5G'0 !4 22! ! *( ' !"( !.5* !*/ 0! & -.9 -! 5 ' 2!22! " !"4 !.5* !* !! ! !5 ! - !!5 ν !! '.& ! 1 ! !"#5* 6& hν =! ". " "( "40& - !!5 3 "( ! ! "(! * "-& . γ ."-& % ! ! -!05 !# !'"-( ! ! ! ! '"-.( ! (! !0"(!# 01& ! ) ( !"!! '"-()5 &- -! 22! ! 0J( (! ( " (!#-! 2! !(! ( ! ! !#4 ! 0".! !"# & hν ! ! "- ! ("# %"- ! "# "-!# "( ! ' 5 6"#& ! ! !"# ! !.; =&;!& "( (' "# &ME=(pc)2 + (m0 c2 )2 .AN,- .- / )(! I.-<- =(/ 522) :? !# "(! ! & - !65 ! ! ( 5pc2υ=EAO.C ! ! -!!# -! 2! ! ( !#4 ! 9 ' AO"- ! E = pc -! -! 2"5 AN ! 5-! 2! "4MAABm0 = 0.% ! !! !"- 2! ! 0"#; ! * "!.5* - !6 "! ! * !5* !"-! "(9 0' "# 2! p=E=chνcAAA, " ! " !( !C " ! "& ! !5 ! !& .!& ! ! !#kx =2πλcos α,ky =2πλcos β,kz =2πλcos γ,AAI λ 3 " "5 cos α cos β cos γ 3 "(41 5 A ! -! ! k = 2πν/c 5 AAA "( "# 2! ! 05!# ' !.& 2Mzkp=h2πk.AAK% "!! ; "#'!.h = 1,05 ×( 0'- =γβyαx2 ' % ?D80 ,1 1 ?"! !!!# -! ! "& 5 "("# 2! "-!# *( ' !'5 <" 0 ! ! E = ω) 0'& +6 !"& 0"!!& " '- A ?/ "0& 5 " !& ! !! ! -! 5 !"( 0 ! ' - !6 & E "# p ! -! 0 & "# ! ! "! *! ! -!( * 2! ( * =!! 6 -(! ( ' *( "# Mω + E = ω + E ,AA k + p = k + p .AA 0+( - !# ' # !! !! " ( !".( ( 3 "% !* (* " !# !"5 "1 !ω = 0, k = 0) '"- ω = 0, k = 0) ( ω = 0ω = 0 k = 0 k = 0)< - !# !;( AA AA 0 22! .! !! -! 5 "#'" ' *( AA "( 0J( ( 2!22! 9 05" E = −Aвых ω =mυ 2max= 0 E = D *( "# (" ( ! 2 !" ";# ! -! # "# 2! " ( !"" 6"% ( 22! ! " ! - ! (!!.22!< " !"( ! ! ( "! '.-! !# ! 05!# -# 0"#;& ?"!"# -.!5!# "(! ! ' ! "# - !65 ! .
! ?" ! ! !"# ! !- ( ( "!1 ( !#4 2π× 10−27 эрг · с =! (' ! 0"#.; '- ! ! .( - !! ω = 2πν "#'(!4 - !! ω -!4 !(4 <" "- ".41 5( "( ."# 2!ME = ω,p = k.AA 8"5 AA ("(4! ( 5 ( !& !! / ('54! 4 "# 2! !! ! -.!!& "& "5 " & *!- & "5 " !( !& "(! ( ! kIE =m0 c21 − (υ/c)2 "#p =− m 0 c2 ,AA.AAm0 v1 − (υ/c)29 '5 *( "# 4! 12,ω = ω + m0 c −1 + 1 − β2k = k +m0 v,1 − β2 "#' 05- 0'- β = υ/cAANAAO,- .- / )(! .->- =: *$F ' ' AAN -! ω > ω ! !! !! .! ! '" # λ > λ !-" # 5; " " - & "! - !! ( ! " .!# - !!& ! 41 "!9! 2! -! ω < ω !# ( " ! ' *( . 1) < ! " '!!# -! υ → 0 ! ( ω → ω 5" - !! '"-( ( '! (D5 *( 2 AAN AAO '"(4! &! ' !# "5 "5 ( '"-( ! " (( 7 "55" '- I '" ? 4!M7 !# -! !5 !"( (! ( ' ".