karlov-kirichenko-kvantovaya-mekhanika-2016 (810755), страница 12
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. ,1m( <; 0"'& 2 5& !M11N = R 2 − 2 , m = 4, 5, 6, . . . ,3( @!MN =R( <2M42N =R152−−m21,m = 5, 6, 7, . . . ,,m = 6, 7, 8, . . .m= 13,6 % <*( ' # ! - !!5 ! " "5ω = 2π c/λ * 2" G!6 ! 5 "-( 5 !(& G0Mme e44π c3= 109737,3 −1 .m2< ! " ! '- !(& G0. R % G!6 0J" " ! ( & 55* & 2"&M11N = R 2 − 2 , n = 1, 2, 3, . . . , m > n. n22n% "* 2"* '0 '& 5 0'-" "! me ) D- - " # 0"' .!"# & '-4 !(& G0 K ?*.
* !-41( !5 !"#5 ( ' 1R=m12me e4AKOn=6n =5n =4ñåðèÿ Áðåêêåòàmn=3Nñåðèÿ ÏàøåíàHα6563Hβ4861n =2Hγ4340ñåðèÿ Áàëüìåðà3647λ, A2 $ ) &) ) + @,1DA =+- 0 0 B 4 15 =! 2" 05" !" "' !"#5*5* AOBN '" ("( !& * 9! 2! -! ! *; 5" !"#5 ' ! " 5 "# -! !-! .! "0 2'- 5 " 7 5! " - 0J( ( " *C " (!# -! (( !"#( "( !# '"#.!! ( " "1( * ! ' !5* & g m) & g n) ( !n=1ñåðèÿ Ëàéìàíà2 $ ) 0) , ) 0B -?80 D) ) )/!- '( '(! ( & !- !#4 <! ! *; !# !4 ! D # !. -!# -! !4 ! '"#!!5 !& !"#*; " ! 05" & & .!(&M '- '( "! 0" # ' 5! )"" 5 3 ' 5! E"" !(& <" 3 ' 5! 2!.22! ! ,- 9- M ( : "+& 9-9- M(/ C*J 8( ' "! 0!# -! ";& ! 5.41& 6 !& " & " 0J( !# * "!.
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" 65* 6 * 0 ""5* 0 '!- * !"(* - !6 = 6"#5& & ' # ! 5 " ' "# ';.( ( & - !65 =! ' / # '(!5& 0 ! ( ' - ! G-# ! ";# (! !(* ! ( 0"#; ! 0"# 5* 41* 4 4 & !5 .4! ( !;4! ( - ! -! !- "-.! '05* & "- ! ! '0 #;! ( 6"# 8#. ! ! 6 !# !∞if0fω = f (t) exp (iω t) d t =,0ω − ω0 +i2τ! !-! 5& !- & !∞11|fω |2 =,|fω |2 dω = 1.2πτ (ω − ω )2 + 104τ 2−∞,- 9- M ( : "+& 9-<- ?) `*=! ' !( "6 ( 2 " ? & 5 !"." # '- !"( - !6 ' (1 C ; " 5 !5 ! !& ω = ω0 ±1/2τ !"(! Δω = 1/τ -! " 05!# ! ! ! " ! !* 3 ! ? !."& !5 ! ' 05! ( !& " "5"(& & "! ! "M*, 8 ?"! -!# -! *! "; ! !' '."-( !- ' ! ! 5 !! ?1 ! -! ! !' '"- 0"4! ( ( ".! 5;! !& "& *!& "( 1 !!! !- & "-5 ( "! " 5;! ! "- !'! ! '5 *! !- '"- /! '5! ( ! -! *! "( 1 ! !! ?! ("(! ( ";5 =! '"- 5"(! *!.- !! ' "#* *!5* "& 5& "! !; "5& !"# 1& ! *! !-. '"-( - ' ! ! *- !((=! ' !"-! ! & ! ! !- !"# !!0 - ! '0 !* "!< " *! !- '"-( '" # -! !"#5 " 4! ( ?( !"( ' *"-" K "41 3 L M N ! A?!"#5 ' ! '"-( ! !.
'* " " ! 05!# -5 0' "#.'5 ! " "!& !!5 "5* !/!- & ! ! "(! ( ;* "!. =! !! ( 0 ( 5 " (!# -! ! !5 '5* *- * (* !4! '"-4.1 ( !- !5 %! "!5 "! !. ("(4! ( !- * !* ";# !"# "# .! "(4! ;* "! 7 ! ! "!5 ("(4! ( ! * !* ' ! ! "- '4! 05- !. ! "! 0041* !5& !! '.( !& !"#5* "! * * !# !! *(! "-&5 0' ' ! /0'41.( ! '"- !"(! 0& "-&4 "!"# !#!* "# '& "!"# ! 0"! ";5 !?";& ! !' '"-( ! IIKβKα50 êÂ30 êÂ40 êÂ25 êÂ30 êÂ20 êÂ15 êÂ0,040,06a0,080,10 λ, íì0,050,150,20λ, íìá2 $$ c )+1 11 +,- =,- )D1 @AE 4 =,- )=1 @"A !& "& " "5 - ! "5* "hν = eV.A K*/ 6 E2G! "- 3 ! # 5 - !! "!!'"- =( ! -# "# !5 (- ' 0"#; ! ! ?"!"# ! *! !.- ! '"-( ! ( !& 5*6& !! ! 5;41* !4 ! % ( ' !& ! ".! ! (' ' * 26 0" 5 ! ! ( ! '"-(! 0" -5 - ! ! 4! ( !& C ! !"!# -! ! "!5 " 0"' ! (0" - ('5 4! - ! !* 6 *> )'" AOAK : AOA * !" -! - !!5 "& *!.
!- ! ! ('5 (5 !. Z !;√ν = A(Z − σ), A σ 3 "-5 *(41 '- "* & !& "( * "! (41 ( * ! ,"( K . - " σ = 1 "( L. σ = 7,5 D )'" !.41& "&4 ' !# ' - !!5 !5"(! ( 7 !"# -! 05" "#' "(,- 9- M ( : "+& 9-<- ?) `*!-( ( "( "! * '"# "(0( 15* "! !0"65 )"%5; (' 0 & 0 !. 05" '- -! !! !41 !;( "#'!# 6-5 "( !* "! !("5* ! % !! !KO ( "! 0 ! !! ( ." * !"# !! ! -! "!5 - !41 .** '!4 - !# (! "5* !((* ! ( !# ( #; ? 05 (" 5 !"." # "' "!5* 0! ! ?" '5 "5 !# 2" "41 0'M11ν = R(Z − σ)2 2 − 2 .me e4 Z 222n2, n = 1, 2, 3, . .
.?!! ! 5 05 '" -! ** '"-5 .( '4! !"#5 " - !!5 !5* "5 "!#"√11ωnm = En − Em = RZ 2 2 − 2 , "νnm = AZ.mn?('# ! 6- 5( 2"& )'" - 7 2." 3 !"# 6 / -!5! & !( *"! 2" )'" !# -5& -" 01& "( *! - & !5 "! -( AA. hi," ! -! !(41 & ! ! ( 5& '!5* "! "0" & ! !"#5* "! =! .41 & ! 2"# -!5! ( #; Z !4"- σ 2" )'" 0" ( "! ! "#& ! ( ! "0 41 & ! !"#5* "!?"!"# ( K 0(' * & !.& "! F! -! ! "!"(! ( 1 ! 6"& "& K M Kα Kβ Kγ ! @" !"( (!#.! "! .! ( "# ,"( L.
σ = 7,5 ! ?"41 0" ( 3 M N O 3 !-4! 1 0" "5 95( ! '"- '-41 !! ! '"-0"#;& #;& "& "5 '" ! & !. 0"( '"-4 41& 0 ! !* '"-&% !! ! '5 "- σ '54! 1 - ! 0J( !# '- σ "41 0' 0! ' " K ! ! *!# ( "! < " ' * !! ( % '"#!! *.5 K . "& 1 !"(4! ( " - !- ( ! '( Z − 1 =! !-! '-4 σ = 1 -! " !-! .!"#5 5?"& L 1! N "! <! K . L. "(* ! ( N = 8 + 2 = 10 "! < ** !5& # !" 22!5& '( ! ! !# Z − (N − 1) = Z − 9 ' !* & "! -! σ = 9 % & !!"# ! σ = 7,5 ! ! ('! * !!- & 6& ! =!nm/! 4 ' "! ' )'" % # 5 ("(! ( ! 0 !(!"# ! -! '- σ '& '5! ( ! "( * "!D-! ! 5 "! !5 !'5* "! ?"!"# "# !( "!( ! ! !"(! 0& !# "!"#5* ""! 41* ( <5& ' * 3 ! 0"&;& ("& K '! ! "& L '! 3 M ! =! -# 5& 5 "( !( "!"#& ! !?* * !-41* !5 !"#5 "( .( *! !- ! '"-( ' - ! Íåïðåðûâíûé ñïåêòðKgLbMKbLaLL- ñåðèÿKaMaÂîçáóæäåíèå K- ñåðèèEn = −A ÂîçáóæäåíèåL- ñåðèèA KK- ñåðèÿ2 $' 0-1 11 +,- :,+ ) K B LB MA N,- 9- M ( : "+& < !# ."0 ; '& ! "! 5 ' "( K /0.';( ( ( '"(! ( !! !41 * .! ! " K "0 0 "! "0 "! '" L M ! -! ! 4.! "4 K .