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Display information for equation id:math.1587.53 on revision:1587
* Page found: Schrödingergleichung mit äußeren Potenzialen (eq math.1587.53)
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\frac{\hbar }{i}\nabla \Psi \acute{\ }(\bar{r},t)=\frac{\hbar }{i}\nabla \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\{ \frac{\hbar }{i}\nabla \Psi (\bar{r},t)+e(\nabla G(\bar{r},t))\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"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">ℏ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></mfrac></mrow><mi mathvariant="normal">∇</mi><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><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">ℏ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></mfrac></mrow><mi mathvariant="normal">∇</mi><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><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi data-mjx-alternate="1">ℏ</mi></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></mfrac></mrow><mi mathvariant="normal">∇</mi><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>+</mo><mi>e</mi><mo stretchy="false">(</mo><mi mathvariant="normal">∇</mi><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><mo stretchy="false">)</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></mstyle></mrow></math>
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