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Ψ x)=√ 1 d 2π kΦ k)eikx, Φ k)=√ dxΨ x)e−ikx, dx|Ψ x) 2π |2= dk|Φ k)|2
1 Ψ x)=(2π 3
1 d
2
3kΦ k)eik·x, Φ k)=(2π 3
d
2
3xΨ x)e−ik·x, d3x|Ψ x)|2= d3k|Φ k)|2
1 ∞
2π eikx 1 dx=δ k),
−∞
∞
eik·xd3x=δ 3)(k) (2π 3 −∞
+∞
dxexp
−∞
−ax2+bx = π
a exp b2
, whenRe(a)>0. 4a
•Wavepackets
dω vgroup = , ∆k∆x k ≃1, shapepreserving: t∆v d ≤∆x
•Hermitianconjugation:
d KΨ x,t))∗Ψ x,t) = dxΨ∗ x,t)(K†Ψ x,t)