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* Page found: Formaler Aufbau der Quantenmechanik (eq math.2711.130)

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\hat{A}=\hat{A}\left( t \right)\Rightarrow {{\left\langle {\hat{A}} \right\rangle }_{t}}=\left\langle \Psi \left( t \right)\,\underbrace{\left| \hat{A}\left( t \right)\, \right|}_{\text{Intrinsisch}}\,\Psi \left( t \right) \right\rangle =\left\langle \Psi \left( 0 \right)\,\underbrace{\left| {{e}^{\mathfrak{i} \hat{H}t}}\hat{A}{{e}^{-\mathfrak{i} \hat{H}t}} \right|}_{{{{\hat{A}}}_{H}}\left( t \right)}\,\Psi \left( 0 \right) \right\rangle

TeX (checked): 

{\hat {A}}={\hat {A}}\left(t\right)\Rightarrow {{\left\langle {\hat {A}}\right\rangle }_{t}}=\left\langle \Psi \left(t\right)\,\underbrace {\left|{\hat {A}}\left(t\right)\,\right|} _{\text{Intrinsisch}}\,\Psi \left(t\right)\right\rangle =\left\langle \Psi \left(0\right)\,\underbrace {\left|{{e}^{{\mathfrak {i}}{\hat {H}}t}}{\hat {A}}{{e}^{-{\mathfrak {i}}{\hat {H}}t}}\right|} _{{{\hat {A}}_{H}}\left(t\right)}\,\Psi \left(0\right)\right\rangle

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A^=A^(t)⇒⟨A^⟩t=⟨Ψ(t)|A^(t)|⏟IntrinsischΨ(t)⟩=⟨Ψ(0)|eiH^tA^e−iH^t|⏟A^H(t)Ψ(0)⟩
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Identifiers

  • A^
  • A^
  • t
  • A^t
  • Ψ
  • t
  • A^
  • t
  • Ψ
  • t
  • Ψ
  • e
  • i
  • H^
  • t
  • A^
  • e
  • i
  • H^
  • t
  • A^H
  • t
  • Ψ

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