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Bestimmung von Segregationspro len in InxGa1-x As ...

Bestimmung von Segregationspro len in InxGa1-x As ...

U(r) = 0 ∂ ˜

U(r) = 0 ∂ ˜ Ψ(r) ∂z ˜Ψ(x, y, z + ɛ) = e ɛ i = ∆xy 4πk0 ˜ Ψ(r) i ∆xy 4πk0 Ψ(x, ˜ y, z) ɛ ˜ Ψ(x, y, z) ∆xyΨ(r) = ∆xy ˜Ψ(q)e 2πiq·r d 3 q = (−4π 2 q 2 ) ˜ Ψ(q)e 2πiq·r d 3 q i e ɛ i ∆xy 4πk0 Ψ(x, ˜ y, z) = e ɛ ∆xy 4πk0 Ψ(x, ˜ −1 − y, z) = F [e iπ k 0 ɛq 2 n i (ɛ 4πk0 ˜Ψ(q)] = e iπk0 x2 +y 2 ɛ ) n ∆ n xy ˜ Ψ(x, y, z) ⊗ ˜ Ψ(x, y, z) Pɛ(x,y) ˜ Ψ(x, y, z) Pɛ(x, y) ɛ lim ˜Ψ(x, y, z + ɛ) = e ɛ→0 ( i ∆xy+i 4πk0 π U k0 (ɛ) (x,y))ɛ ˜Ψ(x, y, z) e ( i ∆xy+i 4πk0 π U k0 (ɛ) i (x,y))ɛ ∆xyɛ 4πk = e 0 Pɛ π i · e U k0 (ɛ) (x,y)ɛ Gɛ ·e h 1 i − ∆xy,i 2 4πk0 π U k0 (ɛ) i (x,y) ɛ2 A B [A, B] = AB − BA C0 = A C1 = B C2 = − 1 2 [A, B] e A+B = e Cn n · . . .

ɛ ɛ zges N−1 N ˜Ψ (ɛN ) (x, y) = P (ɛN ) ⊗ [G (ɛN ) · ˜ Ψ (ɛN−1) (x, y, z)] = F −1 [F (P (ɛN ) )F [(G (ɛN ) · ˜ Ψ (ɛN−1) (x, y))]] ɛ 2 e i ∆xyɛ i 4πk0 · e π U k0 (ɛ) (x,y)ɛ − · e 1 h 2 i ∆xy,i 4πk0 π U k0 (ɛ) (x,y) i ɛ2 = e 1 2 i ∆xyɛ i 4πk0 · e π U k0 (ɛ) 1 i (x,y)ɛ ∆xyɛ 2 4πk · e 0

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