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Display information for equation id:math.1587.59 on revision:1587
* Page found: Schrödingergleichung mit äußeren Potenzialen (eq math.1587.59)
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Hash: dad9efe92b8a91b98fbdd73ec870f492
TeX (original user input):
i\hbar \frac{\partial }{\partial t}\Psi \acute{\ }(\bar{r},t)=i\hbar \frac{\partial }{\partial t}\left\{ \Psi (\bar{r},t){{e}^{i\frac{e}{\hbar }G(\bar{r},t)}} \right\}={{e}^{i\frac{e}{\hbar }G(\bar{r},t)}}\left\{ i\hbar \dot{\Psi }(\bar{r},t)+e\dot{G}\Psi (\bar{r},t) \right\}
TeX (checked):
i\hbar {\frac {\partial }{\partial t}}\Psi {\acute {\ }}({\bar {r}},t)=i\hbar {\frac {\partial }{\partial t}}\left\{\Psi ({\bar {r}},t){{e}^{i{\frac {e}{\hbar }}G({\bar {r}},t)}}\right\}={{e}^{i{\frac {e}{\hbar }}G({\bar {r}},t)}}\left\{i\hbar {\dot {\Psi }}({\bar {r}},t)+e{\dot {G}}\Psi ({\bar {r}},t)\right\}
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<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><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><mi mathvariant="normal">Ψ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</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><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><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><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">ℏ</mi></mrow></mfrac></mrow><mi>G</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></mrow></mrow></msup><mo data-mjx-texclass="CLOSE">}</mo></mrow><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">ℏ</mi></mrow></mfrac></mrow><mi>G</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></mrow></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mi>i</mi><mi data-mjx-alternate="1">ℏ</mi><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><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>G</mi><mo>˙</mo></mover></mrow></mrow><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></mstyle></mrow></math>
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