melbla Atm- ch Känfysik Rybe: ν = 1 λ = R ( 1 n 2 1 m 2 ) Z 2 E n = hcr Z2 n 2 hcr = m e(e 2 /4πɛ ) 2 2 2 = 1, 66 ev M R = R m e + M (massk.) Alkalilika system, me n = n δ l : E = hcr (Z eff ) 2 E S = Vätelika atme: n 2 Z 2 i Z2 (n ) l(l + 1) α2 hcr V () = Ze2 4πɛ = Ze2 a = 2 4πɛ m e e 2 ( Bhs atmmell: n = a n 2 /Z) Raialfunktine, R n,l = P n,l, fö vätelika system: ( ) /2 Z R 1, = a 2e Z/a ( ) /2 Z R 2, = 2a 2(1 Z 2a )e Z/2a ( R 2,1 = ) /2 Z 2a Kltytefunktine Y m l 2 Z 2a e Z/2a = Y l,m Y = 1 4π Y1 = 4π cs θ Y 1 ±1 = sin θe±iϕ 8π 5 Y2 = 16π ( cs2 θ 1) 15 Y 2 ±1 = sin θ cs θe±iϕ 8π 15 Y 2 ±2 = 2π sin2 θe ±2iϕ 1 Hamiltnpeat fö fleelektnsystem: H = i=1 ( 2 2m 2 i Ze2 /4πɛ i + j>i l1 LML l1 LML L = LML L LML LS-kpplin: teme nivåe L(L + 1) { L = l1 l 2,..., l 1 + l 2 S = s 1 s 2,..., s 1 + s 2 = L S,..., L + S e 2 /4πɛ ) ij Zeemaneffekt: µ B BM (en. finstuktu) E ZE = µ B BM (svat fält, hfs) µ B BM + AM M (stakt fält, µ B B > A) Kpplin manetiskt mment öelsemänsmment: S = 2 = 2 + S(S + 1) L(L + 1) 2( + 1) = ( + 1) + ( + 1) ( + 1) 2 ( + 1) µ = µ Dpplebe: ω D = 2 ln 2 u ω c 1, 7u c T u = 22 M m/s Hypefinstuktu: H = µ B e = A ö s-elektne i vätelika system älle: A = 2 µ S µ B µ Z Bltzmanföelninen: 2 1 = 2 1 e E/(kT ) πa n Hamniska scillatn: φ n = 1 ( ) 1/4 mω mω H n (ξ)e ξ2 /2, ξ = 2n n! π x E n = ω(n + 1 2 ) H (ξ) = 1 H 1 (ξ) = 2ξ H 2 (ξ) = 2 + 4ξ 2 H (ξ) = 12ξ + 8ξ H n+1 (ξ) = 2ξH n (ξ) H n(ξ)
nteale Opeate x n e αx x = n! α n+1 x 2n+1 e αx2 x = n! e αx2 x = 1 2 x 2n e αx2 x = p = i L = i H = 2 2m 2 + V 2 = 1 2 2 + 1 2 π α 2α n+1 (2n 1)!! 2(2α) n π α (stana) ( 2 θ 2 + 1 tanθ θ + 1 sin 2 θ 2 ) ϕ 2 Diacntatin: < H >=< ψ H ψ >= ψ Hψv Kmmutate: [A, B] = AB BA [A, B] = [B, A] [A, B + C] = [A, B] + [A, C] [AB, C] = A[B, C] + [A, C]B Schöineekvatinen: R Hψ = Eψ (tisbe.) Hψ = i t ψ (tisbe.) Knfiuatin ni l wi i Teme L ch S ( 2S+1 L) ivåe Tillstån (ZE-subnivåe) M Hypefinivåe 1 =, ±1 ( = = ) nivå 2 M =, ±1 (M = M j = m = ) tillstån byt paitet knfiuatin 4 l = ±1 5 L =, ±1 (L = L = ) tem 6 S = tem 5, 6 baa m L ch S ä a kvanttal. finstuktu - LS hypefinstuktu - växelvekan βl S A mment = L + S = + eentillstån LSM M enei β/2 ( ( + 1) L(L + 1) S(S + 1) ) A/2 ( ( + 1) ( + 1) ( + 1) ) intevall E E 1 = β E E 1 = A (m E S O E e ) (m A E kvaupl ) 2
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