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Display information for equation id:math.1590.4 on revision:1590
* Page found: Kontinuitätsgleichung (Quantenmechnik) (eq math.1590.4)
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Hash: e90a3c5fad10075b05091a845f2fe182
TeX (original user input):
\begin{align}
& i\hbar \frac{\partial }{\partial t}{{\left| \Psi (\bar{r},t) \right|}^{2}}=i\hbar \frac{\partial }{\partial t}\left( \Psi (\bar{r},t)\Psi *(\bar{r},t) \right)=\Psi *(\bar{r},t)i\hbar \frac{\partial }{\partial t}\Psi (\bar{r},t)+\Psi (\bar{r},t)i\hbar \frac{\partial }{\partial t}\Psi *(\bar{r},t) \\
& i\hbar \frac{\partial }{\partial t}{{\left| \Psi (\bar{r},t) \right|}^{2}}=i\hbar \left( \Psi *(\bar{r},t)\dot{\Psi }(\bar{r},t)+\dot{\Psi }*(\bar{r},t)\Psi (\bar{r},t) \right)=\Psi *\hat{H}\Psi -\Psi (\hat{H}\Psi )* \\
\end{align}
TeX (checked):
{\begin{aligned}&i\hbar {\frac {\partial }{\partial t}}{{\left|\Psi ({\bar {r}},t)\right|}^{2}}=i\hbar {\frac {\partial }{\partial t}}\left(\Psi ({\bar {r}},t)\Psi *({\bar {r}},t)\right)=\Psi *({\bar {r}},t)i\hbar {\frac {\partial }{\partial t}}\Psi ({\bar {r}},t)+\Psi ({\bar {r}},t)i\hbar {\frac {\partial }{\partial t}}\Psi *({\bar {r}},t)\\&i\hbar {\frac {\partial }{\partial t}}{{\left|\Psi ({\bar {r}},t)\right|}^{2}}=i\hbar \left(\Psi *({\bar {r}},t){\dot {\Psi }}({\bar {r}},t)+{\dot {\Psi }}*({\bar {r}},t)\Psi ({\bar {r}},t)\right)=\Psi *{\hat {H}}\Psi -\Psi ({\hat {H}}\Psi )*\\\end{aligned}}
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data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><mi mathvariant="normal">Ψ</mi><mo>*</mo><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>i</mi><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>t</mi></mrow></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi mathvariant="normal">Ψ</mi><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mi>i</mi><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">Ψ</mi><mo>*</mo><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">Ψ</mi><mo>˙</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">Ψ</mi><mo>˙</mo></mover></mrow></mrow><mo>*</mo><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mi mathvariant="normal">Ψ</mi><mo 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