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Display information for equation id:math.1594.3 on revision:1594
* Page found: Kontinuitätsgleichung (Quantenmechnik) (eq math.1594.3)
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Hash: b2341cefbea691a1a530ecd094d3ec20
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i\hbar \dot{\Psi }*(\bar{r},t)=\frac{1}{2m}\left[ -{{\hbar }^{2}}\Delta \Psi *-i\hbar e\nabla \left( \bar{A}\Psi * \right)-i\hbar e\bar{A}\left( \nabla \Psi * \right)+{{e}^{2}}{{A}^{2}}\Psi * \right]+V\Psi *(\bar{r},t)
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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"><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><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mo>−</mo><msup><mi data-mjx-alternate="1">ℏ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Ψ</mi><mo>*</mo><mo>−</mo><mi>i</mi><mi data-mjx-alternate="1">ℏ</mi><mi>e</mi><mi mathvariant="normal">∇</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mi mathvariant="normal">Ψ</mi><mo>*</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mi>i</mi><mi data-mjx-alternate="1">ℏ</mi><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>A</mi><mo>¯</mo></mover></mrow></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi mathvariant="normal">∇</mi><mi mathvariant="normal">Ψ</mi><mo>*</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>+</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi>A</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi mathvariant="normal">Ψ</mi><mo>*</mo><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>+</mo><mi>V</mi><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></mstyle></mrow></math>
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