Chapter 1 Quantum kinetic equations: an introduction

Example of observables
➠ Ex1. Position operator: X : ψ → xψ(x).
Observation = Mean particle position:
(ψ, Xψ) = x |ψ| 2 dx
➠ Ex2. Momentum operator P : ψ → −i∇ψ
(ψ, Pψ) = − ψ i∇ψ dx = k | ˆ ψ(k)| 2 dk
ˆψ(k) = Fourier transf.
= (2π) −d/2 e −ik·x ψ(x)dx
(Summary) Pierre Degond - Quantum fluid models - Cetraro, sept 2006
(Conclusion)
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