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Display information for equation id:math.1643.28 on revision:1643

* Page found: Dynamik im Schrödinger- Heisenberg- und Wechselwirkungsbild (eq math.1643.28)

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TeX (original user input): 

\begin{align}
& \left[ \hat{H},{{{\hat{x}}}_{k}} \right]=\frac{\hbar }{i}\frac{\partial \hat{H}}{\partial {{{\hat{p}}}_{k}}}=\frac{\hbar }{i}{{{\hat{x}}}_{k}}^{\circ }\Rightarrow {{{\hat{x}}}^{\circ }}=\frac{\partial \hat{H}}{\partial \hat{p}}=\frac{{\hat{p}}}{m} \\ 

& \left[ \hat{H},{{{\hat{p}}}_{k}} \right]=-\frac{\hbar }{i}\frac{\partial \hat{H}}{\partial {{{\hat{x}}}_{k}}}\Rightarrow {{{\hat{p}}}^{\circ }}=-\frac{\partial \hat{H}}{\partial \hat{x}}=-\nabla V\left( {\hat{x}} \right) \\
\end{align}

TeX (checked): 

{\begin{aligned}&\left[{\hat {H}},{{\hat {x}}_{k}}\right]={\frac {\hbar }{i}}{\frac {\partial {\hat {H}}}{\partial {{\hat {p}}_{k}}}}={\frac {\hbar }{i}}{{\hat {x}}_{k}}^{\circ }\Rightarrow {{\hat {x}}^{\circ }}={\frac {\partial {\hat {H}}}{\partial {\hat {p}}}}={\frac {\hat {p}}{m}}\\&\left[{\hat {H}},{{\hat {p}}_{k}}\right]=-{\frac {\hbar }{i}}{\frac {\partial {\hat {H}}}{\partial {{\hat {x}}_{k}}}}\Rightarrow {{\hat {p}}^{\circ }}=-{\frac {\partial {\hat {H}}}{\partial {\hat {x}}}}=-\nabla V\left({\hat {x}}\right)\\\end{aligned}}

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MathML (34.728 KB / 3.896 KB) :

[ H ^ , x ^ k ] = ℏ i ⁢ ∂ ⁡ H ^ ∂ ⁡ p ^ k = ℏ i ⁢ x ^ k ∘ ⇒ x ^ ∘ = ∂ ⁡ H ^ ∂ ⁡ p ^ = p ^ m [ H ^ , p ^ k ] = - ℏ i ⁢ ∂ ⁡ H ^ ∂ ⁡ x ^ k ⇒ p ^ ∘ = - ∂ ⁡ H ^ ∂ ⁡ x ^ = - ∇ ⁡ V ⁢ ( x ^ ) missing-subexpression ^ 𝐻 subscript ^ 𝑥 𝑘 Planck-constant-over-2-pi 𝑖 ^ 𝐻 subscript ^ 𝑝 𝑘 Planck-constant-over-2-pi 𝑖 superscript subscript ^ 𝑥 𝑘 ⇒ superscript ^ 𝑥 ^ 𝐻 ^ 𝑝 ^ 𝑝 𝑚 absent ^ 𝐻 subscript ^ 𝑝 𝑘 Planck-constant-over-2-pi 𝑖 ^ 𝐻 subscript ^ 𝑥 𝑘 ⇒ superscript ^ 𝑝 ^ 𝐻 ^ 𝑥 ∇ 𝑉 ^ 𝑥 {\displaystyle{\displaystyle\begin{aligned} &\displaystyle\left[\hat{H},{{{% \hat{x}}}_{k}}\right]=\frac{\hbar}{i}\frac{\partial\hat{H}}{\partial{{{\hat{p}% }}_{k}}}=\frac{\hbar}{i}{{{\hat{x}}}_{k}}^{\circ}\Rightarrow{{{\hat{x}}}^{% \circ}}=\frac{\partial\hat{H}}{\partial\hat{p}}=\frac{{\hat{p}}}{m}\\ \par&\displaystyle\left[\hat{H},{{{\hat{p}}}_{k}}\right]=-\frac{\hbar}{i}\frac% {\partial\hat{H}}{\partial{{{\hat{x}}}_{k}}}\Rightarrow{{{\hat{p}}}^{\circ}}=-% \frac{\partial\hat{H}}{\partial\hat{x}}=-\nabla V\left({\hat{x}}\right)\\ \end{aligned}}}

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[H^,x^k]=ℏi∂H^∂p^k=ℏix^k∘⇒x^∘=∂H^∂p^=p^m[H^,p^k]=−ℏi∂H^∂x^k⇒p^∘=−∂H^∂x^=−∇V(x^)

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