: 2005 ( ρ t +dv j =0 r m m r = e E( r +e r B( r T 208 T = d E j 207 ρ t = = = e t δ( r r (t e r r δ( r r (t e r ( r δ( r r (t dv j =

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72 Maxwell. Maxwell e r ( =,,N Maxwell rot E + B t = 0 rot H D t = j dv D = ρ dv B = 0 D = ɛ 0 E H = μ 0 B ρ( r = j( r = N e δ( r r = N e r δ( r r =

: 2005 ( 2006.8.22 73 207 ρ t +dv j =0 r m m r = e E( r +e r B( r T 208 T = d E j 207 ρ t = = = e t δ( r r (t e r r δ( r r (t e r ( r δ( r r (t dv j = e r r δ( r r (t 208 d dt 2 m r 2 = = m r r = e r ( E + r B e r E = d E j E = E( r, B = B( r

: 2005 ( 2006.8.22 74 r Maxwell 209 P = E H E em = d E em E em = 2 (ɛ 0 E 2 + μ 0 H 2 d ( T + Eem + ds dt P =0 P E em ( P 209 Maxwell H rot E + μ 0 H H = 0 E rot H ɛ 0 E E = E j dv ( E H d 2 dt (ɛ 0E 2 + μ 0H 2 = E j dv P + dh em + E dt j =0 dv ( A B = ɛ jk A j B k = ɛ jk ( A j B k + ɛ jk A j ( B k = ɛ kj ( A j B k ɛ jk A j ( B k = rota B A rot B

: 2005 ( 2006.8.22 75.2 dv B 20 2 22 =0 20 X B =rot A X = X T + X L dv X T =0 rot X L =0 X L X T (longtude (transverse X T = rota X L = gradφ 2 X( r = k X k e r dv X = k X k e r rot X = X k e r X L = k e kσ=0 = k, e =, e kσ=2 ( X k e k,0 e k,0 e k r = ( X k k k 2 e r ( X L α = k α k β k 2 X βe r X T = X k σ=,2( k e kσ e kσ e k r = ( X k ( X k k k k 2 e r ( X T α = (δ αβ k αk β k 2 X βe k r = ( ( e kσ α ( e kσ β X β e r σ=,2 σ ( e kσ α ( e kσ β = k αk β k 2 + ( e kσ α ( e kσ β = δ αβ σ=,2 ( e kσ α ( e kσ β = δ αβ k αk β σ=,2 k 2

: 2005 ( 2006.8.22 76 ( rot E + A =0 t v v = ( v e σ e σ v α = v β ( e σ β ( e σ α ( e σ β ( e σ α = δ αβ ψj (xψ j (x =δ(x x j 22 Ω 0 = f dω 0 = fdx :gradf d 2 Ω 0 = j fdx j dx = 0 : rot grad f =0 Ω = A dx : A dω = j A dx j dx :rota d 2 Ω = k j A dx k dx j dx =0 :dvrota =0 Ω 2 = A dx = ɛ jk A dx j dx k : A dω 2 = l A dx l dx = A dx dx 2 dx 3 :dva d 2 Ω 2 = 0 = dx dx 2 dx 3 dx = dx 2 dx 3, dx 2 = dx 3 dx, dx 3 = dx dx 2, (dx dx 2 = dx 3, (dx 2 dx 3 =dx, (dx 3 dx =dx 2, (dx dx 2 dx 3 = A = A dx da = rota =(rota dx d A = dva dφ = gradφ = φ d dφ = Δφ dv rot A = d ( da =d(da =0 rot grad f = d(df =0

: 2005 ( 2006.8.22 77 E = A t φ A φ χ( r, t A A = A + χ φ φ = φ χ t E, B E = E, B = B Maxwell rot H D = j 23 A A ΔA = (dv A + c 2 c φ+μ 2 0 j c 2 = ɛ 0 μ 0 dv D = ρ Δφ =dv A + ɛ 0 ρ dv A =0 Maxwell 2 S L dω 2 = dω = dω 0 = S L A = = μ 0 J Δφ = ɛ 0 ρ Ω 2 : Ω : Ω 0 : S L dv Ad = rot A ds = S A d S A d r grad f d r = f( r r= r fn r= r n 23 μ 0 rot rot A ɛ 0 ( ( A φ = j dv A ΔA + c A + φ = μ 2 0 j

: 2005 ( 2006.8.22 78 J = j ɛ 0 φ 24 φ( r = e 4πɛ 0 r r J = ( t e 4π r r + e rδ( r r 25 dv J =0 A 26 A = A k e k r = 2π L (n x,n y,n z, n =, 2,, 0,, 2, dv A =0 A k =0 27 ˆk e kσ= =0, ˆk e kσ=2 =0, e k e k2 =0 A( r, t = ɛ0 e kσ q kσ (te r σ=,2 24 Δf( r =δ( r f( r = 4πr 25 dv J = t ɛ 0Δφ +dv j = t ρ +dv j =0 26 A k = d A( re r 27 A k = ɛ0 e kσ q kσ (t σ=,2

: 2005 ( 2006.8.22 79 A e = e kσ A = A q (t = q (t φ( r, t = φ k (te k r j( r, t = j k (te k r A = μ 0 J ( dv A =0 ɛ 0 k 2 φ k j k =0 ɛ 0 Δ φ = ρ = r j k 2 φk = j k 28 q kσ + ω 2 k q kσ = ɛ0 e d j( re r = ɛ0 e ( e kσ r e r (ω = ck Maxwell e kσ 28 ( e kσ A( r = e kσ ɛ0 σ=,2 e kσ μ 0J( r = e kσ j( r =μ 0 e kσ j k e k r e kσ ( c 2 q + k 2 q kσ e r = ɛ0 ( c 2 q + k 2 q kσ e r ɛ0 c 2 q + k 2 q kσ = μ 0 ɛ0 e kσ j k = μ 0 d e kσ j( re r

: 2005 ( 2006.8.22 80.3 29 220 E em = d (ɛ 0 ( A + φ 2 + μ0 (rot A 2 2 = E rad + E coulomb E rad = d (ɛ 0 A 2 + μ0 (rot A 2 2 E coulomb = ɛ 0 d (2 A φ + φ φ 2 = ɛ 0 d (2φ dv A + φδφ 2 = d ρφ 2 = e e j 2 4πɛ 0 r r j = <j j e e j 4πɛ 0 r r j +( E coulomb ( E rad p kσ (t = q (t 29 A( r, t = A( r, t = d dv (f g = ɛ0 ɛ0 d f g = e kσ q kσ (te r σ=,2 e kσ p kσ (te r σ=,2 d f g + d fδg = d fδg = d (Δfg d S f g 220 dv (φ A= d S φ A =0 d φdv A = d A φ

: 2005 ( 2006.8.22 8 E rad 22 E rad = 2 T = 2 σ=,2 (p kσ p kσ + c 2 k 2 q kσ q kσ r 2 H = T + E rad + E coulomb q kσ,p kσ, r, P = m r + e A( r =m r + e A H = H part + H rad + H coulomb H part = ( P 2m e A( r 2 = ( P e e kσ q kσ e k r 2m ɛ0 H rad = + (p kσ p 2 kσ + c 2 k 2 q kσ q kσ H coulomb = <j σ=,2 e e j 4πɛ 0 r r j 2 22 H q kσ = ṗ kσ H p kσ = q kσ H r α kσ = P α kσ H P α = ṙ α dv ( A rot A = rota rot A A rot rot A, ( ( A B= A B A B = rota rot A A grad dv A + A ΔA dv A =0 d rot A rot A = d A Δ A

: 2005 ( 2006.8.22 82 222 Maxwell m r = e ( E( r + r B( r 222 ṙ α = H P α = (P α e A α ( r m P α = H r α = m ( P e A( r ( e α A( r +e α φ( r = e ṙ β αa β ( r +e α φ( r r α H coulomb = = r α r α 4πɛ 0 r a r b 4πɛ 0 a<b j( r a r b = α e φ( r = α e φ A = A( r d A dt = d A( r dt + r r A r= r m r α = P α e Ȧ α ( r e r A α ( r = e ṙ β αa β ( r e α φ( r e Ȧ α ( r e r β βa α ( r ( = e α φ( r Ȧα ( r +ṙ β αa β ( r r β βa α ( r ( r rot A α = ɛ αβγ ṙ β ɛ γηξ η A ξ = (δ αη δ βξ δ αξ δ βη ṙ β η A x = ṙ β α A β ṙ β β A α m r = e ( E( r + r B( r

: 2005 ( 2006.8.22 83 223 q + c 2 k 2 q = ɛ0 r = m ( P e A( r e ( r e kσ e r E = A φ = e kσ p kσ e k r φ ɛ0 B =rot A = e kσ q kσ e k r b ɛ0.4 G em 223 ṗ kσ = H q kσ = c 2 k 2 q + = c 2 k 2 q + = c 2 k 2 q ɛ0 q kσ = H p kσ = p q = ṗ = c 2 k 2 q + ɛ0 ( P e ɛ0 e kσ q kσ e k r m ( P m e A ( e ɛ0 e e r e ( r e kσ e r e ( r e kσ e r ( e ɛ0 e e r

= kσ : 2005 ( 2006.8.22 84 G = d P c = d E 2 c H 2 = d ( A + φ rot A c 2 μ 0 = G 0 em + G em G 0 em = d A rot A c 2 μ 0 G em = d φ c 2 μ rot A 0 G 0 em 224 G 0 em = kσ p kσ q kσ ( G em = d (φ c 2 μ rot A φ rot rot A 0 = d φ ΔA c 2 μ = d (Δφ A 0 c 2 μ 0 = d ρa c 2 ɛ 0 μ = e jaj 0 j G T G T = j m j rj + G em = j P j + G 0 em 224 G 0 em = c 2 d μ 0 = c 2 μ 0 ɛ0 = A rot A σ ɛ0 e kσ p kσ ( σ e kσ q kσ σσ p kσ q kσ e kσ ( e kσ p kσ q kσ e ( e =, ( e =

: 2005 ( 2006.8.22 85.5 J em J em = d r P c = d r ( E 2 c H 2 = d r ( A + φ rot A c 2 μ 0 = J em 0 + J em J em 0 = d r ( A rot A c 2 μ 0 J em = d r ( φ c 2 μ rot A 0 J 0 em 225 J em = J em l + J em s J em l = d 3 r A μ 0 c 2 j laj J em s = d 3 r A A μ 0 c 2 = ( e kσ e kσ p kσ q kσ k,σσ 225 (Ȧ rot A =ɛ jk A j ɛ klm l A m =(δ l δ jm δ m δ jl A j l A m =Ȧj A j Ȧj j A = Ȧj A j j (ȦjA + t ( ja j A =Ȧj A j j ( A j A ( r (Ȧ rot A a =ɛ abc r b Ȧ j c A j ɛ abc r b j ( A j A =ɛ abc r b Ȧ j c A j j (ɛ abc r b Ȧ j A +ɛ abc j (r b j (ȦjA c = ɛ abc r b Ȧ j c A j j (ɛ abc r b A j A c +ɛ abc Ȧ b A c = Ȧj( la j a j (ɛ abc r b A j A c +ɛ abc Ȧ b A c d 3 r r (Ȧ rot A= d 3 r Ȧj la j + d 3 r A A

: 2005 ( 2006.8.22 86 226 J em = ɛ 0 d Δφ r A = d ρ r A = r j (e jaj j J T J T = j r j (m j rj + J em = j L j + J 0 em L j = r j (m r j + e j A j = r j P j 2 2. Maxwell 226 A = (dv A + c φ μ 2 0 j c Δφ = c t dv A μ 0 cρ φ rot A = (φrot A φrot rot A = (φrot A+φΔ A r ( φ rot A= r ( (φrot A + r φδa [ r ( (φrot A] =ɛ jk r j ɛ klm l (φrot A m =(δ l δ jm δ m δ jl r j l (φrot A m =r j (φrot A j r j j (φrot A = (r j φ(rot A j φ(rot A j (r j φ(rot A +3φ(rot A = (r j φ(rot A j j (r j φ(rot A +2φ(rot A [ r φδa] =ɛ jk r j φ l l A k = l (ɛ jk r j φ l A k ɛ jk φ j A k ɛ jk r j ( l φ l A k ( = l (ɛ jk r j φ l A k ɛ jk φ j A k l ɛjk r j ( l φa k + ɛjk ( j φa k + ɛ jk r j ( l l φa k ( = l (ɛ jk r j φ l A k ɛ jk φ j A k l ɛjk r j ( l φa k + j (ɛ jk φa k ɛ jk φ( j A k +ɛ jk r j ( l l φa k ( = l (ɛ jk r j φ l A k l ɛjk r j ( l φa k + j (ɛ jk φa k 2φ(rot A +(Δφ( r A J em = ɛ 0 d Δφ r A = d ρ r A = j r j (e j A j

: 2005 ( 2006.8.22 87 227 Maxwell μ ( μ A ν ν A μ =μ 0 j ν A 0 = c φ μ f μν = μ 0 j ν A = A = A x A 2 = A 2 = A y A 3 = A 3 = A z f μν = μ A ν ν A μ j 0 = cρ j =( j (τ ( dτ ( = dt v2 c 2 227 A = (dv A + c φ 2 μ 0 j c Δφ = c t dv A μ 0 cρ dv A + c 2 φ t = μa μ μ μ A = μ A μ μ 0 j 2 c φ + φ c 3 t = ( μ A μ c t c 2 t φ μ 0 cρ μ μ A 0 = 0 μ A μ μ 0 j 0 Maxwell μ ( μ A ν ν A μ =μ 0 j ν μ f μν = μ 0 j ν

: 2005 ( 2006.8.22 88 S em = S 0 + S rad + S el = d 4 x ( L 0 (x+l rad (x+l el (x (d 4 x = dx 0 dx dx 2 dx 3 = cdtd 3 r L 0 (x = dx μ ( dx ν ( m c dτ ( g μν δ 4 (x x ( dτ ( dτ ( S 0 = dx μ ( dx ν ( m c dτ ( g μν = m c dt g μν ẋ μ dτ ( dτ (ẋν ( ( L rad (x = 4μ 0 c f μνf μν S rad = dtd 3 rf μν f μν 4μ 0 L el (x = j μ (xa μ (x S el = d 4 x L el (x = dt e A μ (x ( ẋ μ ( = ( dt e φ( r,t+ r A( r,t j μ (x = ce dτ ( δ 4 (x x ( x μ ( =(c e δ 3 ( r r,e r δ 3 ( r r δl rad δa μ (x = ν 4μ 0 = μ 0 ν f νμ δl el δa μ (x = jμ ( κ A ρ ρ A κ ( κ A ρ ρ A κ ν A μ

: 2005 ( 2006.8.22 89 2.2 Maxwell ( μ f μν = μ 0 j ν f λν 228 μ T μ λ = f λν j ν T μ λ = μ 0 ( f κμ f κλ 4 δμ λf κν f κν T μ λ T μν = g λν T μ λ T μν = ( g λν g κα g λβ f κμ f αβ μ 0 4 gλν δ μ λf κν f κν = μ 0 ( g κα f κμ f αν 4 gμν f κν f κν 228 f λν μ f μν = μ (f λν f μν f μν μ f λν = μ (f λν f μν 2 f μν ( μ f λν ν f λμ, f μν = f νμ = μ (f λν f μν 2 f μν ( μ f λν + ν f μλ + λ f νμ + 2 f μν λ f νμ = μ (f λν f μν + 2 f μν λ f νμ = μ (f λν f μν 4 λ(f μν f μν = μ (f λν f μν 4 λ(f κν f κν = μ (f λν f μν 4 δμ λ μ (f κν f κν ( = μ f κμ f κλ 4 δμ λf κν f κν μ f λν + ν f μλ + λ f νμ = μ ( λ A ν ν A λ + ν ( μ A λ λ A μ + λ ( ν A μ μ A ν =0

: 2005 ( 2006.8.22 90 T μν = T νμ. 229 T 00 = 2 (ɛ 0 E 2 + μ 0 H 2 = H em T k0 = c ( P k, P = E H T kl = ɛ 0 E k E l + μ 0 H k H l δ kl 2 (ɛ 0 E 2 μ 0 H 2 μ T μκ = f κν j ν 229 f μν = E x c E y c E z c 0 Ex c 0 B z B y Ey c B z 0 B x Ez c 0 B x 0 f αβ = g αμ g nuβ f μν E { 0 0 0 0 x E y E z c c c = 0 0 0 Ex c 0 B z B y 0 0 0 Ey c B z 0 B x 0 0 0 Ez c 0 B x 0 0 Ex c Ey c Ez c = E x c 0 B z B y E y c B z 0 B x E z c B y B x 0 μν αβ f αβ f αβ = 2 c 2 E 2 +2 B 2 0 0 0 0 0 0 0 0 0 0 0 0 } αβ T 00 = ( μ 0 c 2 E 2 4 ( 2 c 2 E 2 +2B 2 = 2 (ɛ 0E 2 + μ 0H 2 = H em T 0 = ( B z E y + B y E x = cμ 0 c ( E H T k0 = c P k, P = E H T kl = μ 0 ( c 2 E ke l + B k B l + δ kl 2 ( c 2 E 2 + B 2 = ɛ 0 E k E l + μ 0 H k H l δ kl 2 (ɛ 0 E 2 μ 0 H 2

: 2005 ( 2006.8.22 9 dπμ ( dt d 3 rj ( x= = e x κ( f μκ e x κ( f μκ 230 d dt π μ ( = c d 3 rt 0μ t M c 2 + d 3 r H em ( r =const. M v + d 3 r P ( r =const. 3 q kσ,p kσ, r, P = m r +e A [q kσ,p k σ ] = δ k δ σσ [r α,pβ j ] = δ jδ αβ P = 230 d dt π μ ( = = c t = c t d 3 r ν T νμ d 3 rt 0μ + d 3 rt 0μ + T μ S ds T μ = c d 3 rt 0μ t

: 2005 ( 2006.8.22 92 q kσ = (a 2ω + a kσ kσ k ωk p kσ = 2 (a a [a kσ,a σ ] = δ δ σσ [a kσ,a σ ] = 0 [a,a σ ] = 0 23 A( r = ɛo 2ω k e kσ (a e r + a kσ e r 23 A( r = = = ɛo ɛo ɛo e kσ q kσ e k r e kσ (a 2ω k + a kσ e r e kσ (a e k r + a 2ω k kσ kσ e k r

: 2005 ( 2006.8.22 93 232 [A α ( r,a β ( r ] =0 [E α ( r,e β ( r ] =0 [B α ( r,b β ( r ] =0 [E α ( r,a κ ( r ] = ɛ 0 ɛ αβγ γ δ( r r 3. Hamltonan 232 233 [A α ( r,a β ( r ] =0 [E α ( r,e β ( r ] =0 [B α ( r,b β ( r ] =0 [E α ( r,a β ( r ] = ( e kσ α ( e kσ β [p kσ,q kσ ]e k ( r r ɛ 0 = ( e kσ α ( e kσ β e k ( r r ɛ 0 = (δ αβ k αk β ɛ 0 k 2 e ( r r [E α ( r,b β ( r ] =ɛ βγκ γ[e α ( r,a κ ( r ] = ɛ 0 = ɛ 0 (δ ακ k αk κ k 2 ɛ βγα k γ e k ( r r = ɛ 0 ɛ αβγ γδ( r r ɛ βγκk γ e ( r r 2 233 (p kσ p kσ + ω 2kq kσ q kσ k = k = k = k = k ( ω k (a 4 kσ a (a a kσ +(a + a kσ (a + a ω k 4 (a a + a a kσ +a a +a a ω k 2 (a a + a a kσ ω k (a a kσ + 2

: 2005 ( 2006.8.22 94 234 H = H part + H rad + H coulomb H part = ( 2m e A( r 2 A( r = e kσ (a ɛo 2ω kσ e r + a kσ e r k H rad = k σ=,2 n kσ = a a kσ H coulomb = e e j r r j ω k (n kσ + 2 3.2 235 G 0 em = n kσ 234 A( r = ɛo 2ω k e kσ (a e r + a kσ e r 235 G 0 em = p kσ q kσ kσ = 2 (a a kσ (a + a kσ = 2 (a a a kσ a + a a kσ a a kσ = a a kσ kσ ( (

: 2005 ( 2006.8.22 95 G T = G p + G 0 em = + G p = n kσ 236 [H, G T ]=0 4 A, A 2 237 P A( r = A( r P 236 H = H 0 + H nt [e r j, j ] = e r j [a, a a] = a [a,a a] = a [( A( r α, G T ] = ( ( e kσ α [a e r, 2ω k kσ + n kσ ] ɛ0 +[a kσ e r, + n kσ ] =0 [H part, G T ] = 0 [H, G T ] = [H part + H rad + H coulomb, G p + G 0 em ] = [H rad + H coulomb, G p + G 0 em] = [H coulomb, G p + G 0 em ] = [H coulomb, G p ]=0 237 [ P, A( r ] = A P ( +( P A A ( P = dv A( r =0

: 2005 ( 2006.8.22 96 H 0 H 0 = H p + H rad H p = 2 Δ + e e j 2m r r j H rad = ω k (n kσ + 2 k σ=,2 H nt H nt = H ( + H (2 H ( = = H (2 = = ɛo e m A( r e m (e 2 2m A( r 2 (e 2 2m ɛ o 2ω k (a + a e r ( e kσ ( e kσ e k σ 2 (a ω k ω k + a kσ kσ (a + a k σ σ e ( r + r σσ Ψ m ({ r } E m {n kσ } ( H 0 m; {n kσ } = (E m + kσ n k ω k m; {n kσ } m; {n kσ } = {n kσ } Ψ m ({ r } H p Ψ m ({ r } = E m Ψ m ({ r } H rad {n kσ } = n k ω k {n kσ } kσ H ( H (2 2 e 2m σ rot A

: 2005 ( 2006.8.22 97 H (s = = ɛ0 e σ rot A = 2m e 2m k,σ e 2m σ A 2ω k (a + a e r σ ( e kσ 4. H 0 n = E n n ( H = H 0 + H nt 0 a b t Ψ=(H 0 + H nt Ψ 238 Ψ=e H 0t/ Ψ I t Ψ I = H I ntψ I H I nt = e H 0t/ H nt e H 0t/ Ψ I (t = n c n (t n ċ n = m n H I nt m c m = m n H nt m e (En Emt/ c m 238

: 2005 ( 2006.8.22 98 (? d dt c n (t 2 =0 n c a (t =0=, c n (t =0=0, (n a 239 c b (t = b H nt a e(e b E at/ E b E a c b (t 2 = b H nt a 2 2 cos(e b E a t/ (E b E a 2 240 24 cos αx δ(x = lm α παx 2 a b w a b 242 w a b = t c b(t 2 2π b H nt a 2 δ(e b E a b de b ρ(e b ρ(e b de b w a b ρ(e b de b = 2π b H nt a 2 ρ(e b 243 239 ċ b (t = b H nt a e (E b E at/ c a 240 24 242 b H nt a << E b E a cos αx dy y 2 = π E a E b t >> 243.

: 2005 ( 2006.8.22 99 4.2 m b ; {n kσ } b H ( m a ; {n kσ } a = kσ M p ba (, σ = = M rad ba (, σ = M p ba (, σm rad ba (, σ ( d r Ψ b({ r } e e r ( e kσ m Ψ a ({ r } {n kσ } b (a ɛo 2ω + a kσ kσ {n kσ } a k 244 n a n = n 2ω 2ω 2ω n + a n = n + 2ω Ψ m ({ r } (m = a, b M p ba ( a E k E = ω e2 4πɛ 0 a e 2 k = 2π λ = ω c = E c a 4πɛ 0 c = α a k α a << a, α = e2 4πɛ 0 c 37, α =0 H p 245 [H p, r ]= 2 m [H p,r,α ]= 2 m, α 244 245 [ p2 2m,r]= p 2[p, r] = p 2m 2m 2( = p m

: 2005 ( 2006.8.22 200 M p ba M p,e dpole ba M p,e dpole ba = (E b E a = (E b E a b d r Ψ b ({ r } ( ( e k=0,σ r e a ( e k=0,σ r e Ψ a ({ r } μ T σ,ba = = ω ba μ T σ,ba b μ σ a, ω ba = E b E a b a d r Ψ b ({ r }( Ψ a ({ r }, μ σ = e k,σ μ, μ = e r ( e r b a f ba f ab = 2m M p e 2 ba ω 2 ba 246 f ba =N 246 2 b [ N N [ r,α, [H p, r j,β ]] = N 2m [ N N r,α, [ p 2 k, r j,β ]] j = 2 N 2m [ N r,α, p j,β ] N N 2 ( e σ r, [H p, ( e σ r j ]] =( e σ α ( e σ α j =( 2 ( 2m Nδ αβ = 2 m Nδ αβ k j j m N = 2 m N [x, [H, x]] = [x, Hx xh] =xhx x 2 H Hx 2 + xhx =2xHx x 2 H Hx 2 a [x, [H, x]] a =2 a xhx a a x 2 H a a Hx 2 a =2 a xhx a E a a x 2 a E a a x 2 a =2 a x b b Hx a 2E a a x b b x a b b =2 (E b E a b x a 2 b

: 2005 ( 2006.8.22 20 O( 0 e r + r ( M p ba M p,e d ba + d r Ψ b ({ r e } r ( e k,σ Ψ a ({ r } m 247 ( r( e = 2 ( e l + 2 [H p, ( r( e r] M p ba M p,e d ba M p,e q ba =(E b E a ( M p,m d ba = d r Ψ b ({ r } + M p,e q ba + M p,m d 2 ba ( d r Ψ b ({ r } ( r ( e k,σ r e 2 ( e m 2 ( e kσ l Ψ a ({ r } Ψ a ({ r } M p,e q ba 2 M p,m d ba H (s e k r = M p,m d 2 ba x = e σ r a a = f ba = b b 247 2m e 2 ω ba μ T σ,ba 2 = b 2 e 2 m 2 (E b E a μ T σ,ba 2 = N ( e( r =ɛ jk k j e k ɛ ab r a b =(δ ja δ kb δ jb δ ka k j e k r a b =k j e k r j k k j e k r k j [H p,r r j ]=r [H p,r j ]+[H p,r ]r j = 2 m (r j + j r ( r( e =k r e j j = 2 k e j (r j r j + 2 k e j (r j + r j = 2 ( e ( r + 2 [H p, ( r( e r]

: 2005 ( 2006.8.22 202 ( M p,m d ba = d r Ψ b ({ r } M = l + σ = l +2 s e 2m ( e kσ M Ψ a ({ r } L [E,E + de] ρ(ede dω [k, k + dk] 248 ρ(e = (2π 3 ω 2 c 3 dω 4.3 a E a {n } b E b νn ν + ( ω = E a E b dω σ wdω wdω = 2π ɛ 0 ω2 μ T σ 2 2ω ( n kσ + ρ(e k σ n kσ 248 w = w sp + w nd = w sp = w nd = ω 3 8π 2 ɛ 0 c 3 μt σ 2 n kσ ω 3 8π 2 ɛ 0 c 3 μt σ 2 ω 3 8π 2 ɛ 0 c 3 μt σ 2 ( n kσ + ρde = dkk2 dω ( 2π = k2 dkdω L 3 (2π 3 E = ck ρ(e = E 2 (2π 3 ( c 3 dω = ω 2 (2π 3 c 3 dω

: 2005 ( 2006.8.22 203 n kσ w nd 4.4 n kσ + n kσ ω 3 w a = 8π 2 ɛ 0 c 3 μt σ 2 n kσ I(ωdω 249 I(ωdω = c ωn ρ ωdω =( ( ρ ω dω w a = π ɛ 0 2 c μt σ 2 I(ω a, b (E b E a = ω N a, N b, A a b = A b a N b A b a (n +=N a A a b n N b N a = e (E b E a/k B T = e hbarω/k BT n = e ω/k BT 249 ρ(ede = ρ(ωdω ρ(ω =ρ(e I(ω = 2 ωcn ρ(e

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