ρ ˙ = L ρ = − i ℏ [ H , ρ ] {\displaystyle {\dot {\rho }}={\mathcal {L}}\rho =-{\frac {i}{\color {Gray}\hbar }}\left[{H,\rho }\right]} mit
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Schrödingergleichung
i ∂ t Ψ ( t ) = H ^ Ψ ( t ) {\displaystyle {{\mathfrak {i}}{\partial }_{t}}\Psi (t)={\hat {H}}\Psi (t)}
Dirac Notation
Ket: | i ∂ t Ψ ( t ) ⟩ = | H ^ Ψ ( t ) ⟩ {\displaystyle \left|{{{\mathfrak {i}}{\partial }_{t}}\Psi (t)}\right\rangle =\left|{\hat {H}}\Psi (t)\right\rangle }
i ∂ t | Ψ ( t ) ⟩ = H ^ | Ψ ( t ) ⟩ {\displaystyle {\mathfrak {i}}\partial _{t}\left|\Psi \left(t\right)\right\rangle ={\hat {H}}\left|\Psi (t)\right\rangle }
Bra:
⟨ - i ∂ t Ψ ( t ) | = ⟨ H ^ Ψ ( t ) | - i ∂ t ⟨ Ψ ( t ) | = H ^ ⟨ Ψ ( t ) | , H ^ = H ^ + {\displaystyle {\begin{aligned}&\left\langle {\text{-}}{\mathfrak {i}}{{\partial }_{t}}\Psi \left(t\right)\right|=\left\langle {\hat {H}}\Psi \left(t\right)\right|\\&{\text{-}}{\mathfrak {i}}{{\partial }_{t}}\left\langle \Psi \left(t\right)\right|={\hat {H}}\left\langle \Psi \left(t\right)\right|,\,{\hat {H}}={{\hat {H}}^{+}}\\\end{aligned}}}
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