65 1 1.1 1.1.1 1.1 H H () = E (), (1.1) H ν () = E ν () ν (). (1.) () () = δ, (1.3) μ () ν () = δ(μ ν). (1.4) E E ν () E () H 1.1: H α(t) = c (t) () + dνc ν (t) ν (), (1.5) H () () + dν ν () ν () = 1 (1.6)
66 1 ν k k k 1.1. L k k = π L, = ( x, y, z ) (1.7) k u box (x) = 1 L 3/ exp(i k x) (1.8) L 3 1 1. k z = k y =( x, y, ) k k k+dk dk k k +dk L k x (1.7) k 1.: x y z ( L π ) 3 d 3 k = ( L π ) 3 dkk si θ dθ dφ = ( L π ) 3 dkk dω (1.9) dω = si θ dθ dφ E = k k dk = de L3 x y z 8π 3 k de dω (1.1)
1.1. 67 E E +de Ω Ω +dω ρ box (E)dE dω = L3 k de dω (1.11) 8π3 ρ box (E) E L = L π k (1.1) u k (x) = ( ) L 3/ li u box (x) = L π 1 exp(i k x). (1.13) (π) 3/ (π) 3 ( u k,u k ) = δ(k k ). (1.14) E E +de Ω Ω +dω ρ(e)de dω = k de dω, k = E (1.15) p =k 1 u p (x) = (π) 3/ exp(i k x) = 1 exp (i p ) (π) 3/ x (1.16) (π) 3 ( u p,u p ) = δ(p p ) (1.17)
68 1 1. 1..1 H (x,t) = V (x) e iωt + V (x) e +iωt. (1.18) H(t) (1.5) H c (t) t = c () = δ i, c ν () =. (1.19) c (1) (t) = 1 t i c (1) ν (t) = 1 i t dt V i (t ) = V i e i(ω i ω)t 1 (ω i ω) dt V νi (t ) = V νi e i(ω νi ω)t 1 (ω νi ω) (V i ) ei(ω i +ω)t 1 (ω i + ω) (V iν ) ei(ω νi +ω)t 1 (ω νi + ω) (1.) (1.1) ω i = E() E () i, V i = () V i () (V i ) = () V i () (1.) E ω νi = E() ν E () i V νi = ν () V i () (V iν ) = ν () V i () (1.3) hω E ν () (1.) (1.1) c (1) (t) t () 1.3 ν ν ν +dν c (1) ν (t) dν E ν () >E () i (1.1) ω ω νi = E() ν E () i E i () 1.3: (1.4)
1.. 69 (1.1) c ν (t) dν = [ ] si (ωνi ω)t/ V νi dν. (1.5) (ω νi ω) E ν E ν +de ν ρ(e ν )de ν E ν E i +ω c ν (t) ρ(e ν )de ν = [ ] si (ωνi ω)t/ V (ω νi ω) νi ρ(e ν )de ν (1.6) ρ(e ν ) t [ si (ωνi ω)t/ (ω νi ω) V νi li t ] t π δ(ω νi ω) (t ) (1.7) c ν (t) ρ(e ν )de ν = π V νi ρ(e ν ) t Eν E i +ω. (1.8) t w ν = π V νi ρ(e ν ) (1.9) Eν E i +ω 1.. E H (x,t) = V (x) e iωt + V (x) e +iωt H t = 1.4 1 c ν () = δ(ν ν 1 ) (1.3) hω () E ν () E ν1 c (1) ν (t) = δ(ν ν 1 )+ 1 t dt V νν1 (1.31) i 1.4:
7 1 (1.1) c (1) e i(ω νν 1 ω)t 1 ν (t) = V νν1 (V (ω νν1 ω) ν1 ν) ei(ω νν 1 +ω)t 1 (1.3) (ω νν1 + ω) E ν E ν1 +ω, E ν E ν1 ω (1.33) E ν H ω ω (1.9) w ν = π V νν 1 ρ(e ν ) (1.34) Eν E ν1 +ω w ν = π V νν 1 ρ(e ν ) Eν E ν1 ω (1.35) E ν1 H (t) ω E ν E ν1 +ω 1.4 (1.34) w ν1 ν = π V ν ν 1 ρ(e ν ). (1.36) E ν E ν1 +ω E ν H (t) ω E ν1 E ν ω 1.4 (1.35) w ν ν 1 = π V ν 1 ν ρ(e ν1 ). (1.37) E ν1 E ν ω ν 1 ν ν () V ν() 1 = ν() 1 V ν () V ν ν 1 = V ν1 ν (1.38) w ν1 ν ρ(e ν ) = w ν ν 1 ρ(e ν1 ) (1.39) detailed balace
1.3. 71 1.3 1.3.1 α = e c 1 137 H = H + eφ(x) e c A p (1.4) φ A ε ( ) ω A = A ε cos c x ωt. (1.41) ε = A = (1.4) (1.4) e c A p = e [ c A ε p exp (i ω ) ( c x iωt + exp i ω ) ] c x + iωt (1.43) H (x,t) = V (x) e iωt + V (x) e +iωt (1.44) V (x) = ea ( c exp +i ω ) c x ε p (1.45) V (x) = ea ( c exp i ω ) c x ε p (1.46)
7 1 1.3. t w i = π V i δ(e E i ω) (1.47) w i = π V i ρ(e ) E E i +ω (1.48) (1.41) absorptio cross sectio = (1.49) U U = 1 ( ) E 4π + B (1.5) 4π E B E = 1 c A, B = A (1.51) (1.41) σ abs σ abs = c U = 1 π ω π V i δ(e E i ω) = 4π ω e c 1 ω π c A ( exp i ω )ε c x p i ω c A (1.5) δ(e E i ω) (1.53)
1.3. 73 1.3.3 E = (Zαc) = 1 a B /Z Zαc 1 R Zαc R c ω = E λ = ω/(π) 4πR Zα, R λ Zα 4π α 1/137 (1.53) x R x R ω Zα x c Z exp (i ω ) c x = 1+i ω x + (1.54) c 1 exp (i ω ) c x ε p i ε p i (1.55) p x [ x, H ] = i p. (1.56) z ε x ε p = p x (1.55) ε p i = p x i = i [ x, H ] i [ x, H ] i = ( xh H x ) i = (E () i E () ) x i ε p i = i ω i x i, ω i = E() E () i (1.57) electric dipole approxiatio (1.53) σ abs = 4π αω i x i δ(ω ω i ). (1.58)
74 1 1.3.4 photoelectric effect photoelectro (1.53) (1.11) k f ρ(e)de dω = L3 8π 3 k f de dω (1.59) Ω Ω +dω dσ dω = 4π α ω k f exp (i ω ) c x k ε p i f L 3 (1.6) (π) 3 K k f exp (i ω ) c x ε p i = ε d 3 x ( ) 3/ Z ( ) ( exp ik a B L f x exp i ω ( ) [exp c x i Zr )] a B ε [ ( ε exp i ω ) ] [ ( )] ( ) c x =, exp ik f x = ik f exp ik f x ε q = k f ω c (1.61) dσ dω = (ε k f ) 3e k f cω ( ) 5 Z 1 [ ] a B Z 4 (1.6) ab + q
1.4. 75 1.4 1.4.1 H(t) c (t) i ψ(x,t) = H(x,t) ψ(x,t). (1.63) H(x,t) H(x,t) E ( ψ (x,t) = exp i E ) t u (x) (1.64) E (t) t [ ψ (x,t) = u (x) exp i E (t ] ) dt (1.65) t (1.63) ψ(x,t) ψ(x,t) = t [ c (t)u (x,t) exp i E (t ] ) dt. (1.66) u H(t) u (x,t) dc (t) = ( c dt (t) u, u ) t [ exp i E (t ) E (t ] ) dt (1.67) u H(t)u (t) =E (t)u (t) H(t) u (t)+h(t) u (t) = E (t) u (t)+e (t) u (t) u ( u, u ) = 1 ( u E E, H ) u ( ) (1.68) = ( u,u )=1 ( u, u ) ( u ) +,u = ( u, u ) ( + u, u ) =
76 1 z z + z =Rez γ(t) ( u, u ) = i dγ (1.69) dt dc (t) dt = i dγ (t) c dt (t) ( ) + c (t) 1 ( u E E, H u ) t [ exp i E (t ) E (t ] ) dt (1.7) E E t = u i t u c (t) i ( (E E i ) u, H ) [ u i exp( i E E ) ] i t 1 (1.71) adiabatic approxiatio 1.4. 1.5 / E () E () i H H φ i (x) H φ i (x) = E i φ i (x) (1.7) t H 1.5: φ i (x) H = H + H φ i (x)
1.4. 77 H = H + H Hψ (x) = E ψ (x). (1.73) φ i (x) φ i (x) = c ψ (x), c = (ψ,φ i ) = d 3 x ψ (x) φ i (x) (1.74) ψ (x) w = dx ψ (x) φ i (x) (1.75) sudde approxiatio F Fx H = p + 1 ω x Fx = p + 1 ω (x x ) + C, x = F ω. (1.76) 1.6 x x 1.6 C u (x) u (x x ) V( x) u (x) c u (x x ) = w = c w = [ + dxu (x x )u (x)] (1.77) s = x b, s = x b, b = x 1.6: ω x (1.78)
78 1 H(s) u (x) = ( ) 1 1/4 1 πb /! e s H (s), H (s) = ( 1) e s d e s ds (1.79) + dxu (x x )u (x) = ( 1) +!π e s / + dse s s d e s +s s ds = s + dse s s d e s +s s ds dse s +s s = s πe s /4 w = 1! s e s / = σ! e σ, σ = s = F ω 3 (1.8) 1 w = e σ = = σ! = e σ e +σ = 1. (1.81) w (1.8) σ σ w = e σ σ! = = = e σ σ =1 σ 1 ( 1)! = e σ σ = σ! = σ. (1.8) 1.7 σ =.3 1.5 5. 1 9 8 7 6 5 4 3 1 σ =.3..1..3.4.5.6.7.8 w 1 9 8 7 6 5 4 3 1 σ = 1.5..1..3 w 1 9 8 7 6 5 4 3 1 σ = 5...1. w 1.7: