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Display information for equation id:math.1592.3 on revision:1592

* Page found: Kontinuitätsgleichung (Quantenmechnik) (eq math.1592.3)

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Hash: 5161a968cb28009204db6842ea3e4b70

TeX (original user input): 

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)

TeX (checked): 

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)

LaTeXML (experimental; uses MathML) rendering

MathML (13.108 KB / 2.073 KB) :

i ℏ Ψ ˙ * ( r ¯ , t ) = 1 2 ⁢ m [ - ℏ 2 Δ Ψ * - i ℏ e ∇ ( A ¯ Ψ * ) - i ℏ e A ¯ ( ∇ Ψ * ) + e 2 A 2 Ψ * ] + V Ψ * ( r ¯ , t ) fragments i Planck-constant-over-2-pi ˙ Ψ fragments ( ¯ 𝑟 , t ) 1 2 𝑚 fragments [ superscript Planck-constant-over-2-pi 2 Δ Ψ i Planck-constant-over-2-pi e ∇ fragments ( ¯ 𝐴 Ψ ) i Planck-constant-over-2-pi e ¯ 𝐴 fragments ( ∇ Ψ ) superscript 𝑒 2 superscript 𝐴 2 Ψ ] V Ψ fragments ( ¯ 𝑟 , t ) {\displaystyle{\displaystyle 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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            <ci id="p1.1.m1.1.52.2.cmml" xref="p1.1.m1.1.52.2">𝑟</ci>
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    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle 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)}}</annotation>
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MathML (2.231 KB / 439 B) :

iℏΨ˙*(r¯,t)=12m[−ℏ2ΔΨ*−iℏe∇(A¯Ψ*)−iℏeA¯(∇Ψ*)+e2A2Ψ*]+VΨ*(r¯,t)
<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">&#x210F;</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi mathvariant="normal">&#x03A8;</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>&#x2212;</mo><msup><mi data-mjx-alternate="1">&#x210F;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi mathvariant="normal">&#x0394;</mi><mi mathvariant="normal">&#x03A8;</mi><mo>*</mo><mo>&#x2212;</mo><mi>i</mi><mi data-mjx-alternate="1">&#x210F;</mi><mi>e</mi><mi mathvariant="normal">&#x2207;</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">&#x03A8;</mi><mo>*</mo><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>&#x2212;</mo><mi>i</mi><mi data-mjx-alternate="1">&#x210F;</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">&#x2207;</mi><mi mathvariant="normal">&#x03A8;</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">&#x03A8;</mi><mo>*</mo><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>+</mo><mi>V</mi><mi mathvariant="normal">&#x03A8;</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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Identifiers

  • i
  • Ψ˙
  • r¯
  • t
  • m
  • Δ
  • Ψ
  • i
  • e
  • A¯
  • Ψ
  • i
  • e
  • A¯
  • Ψ
  • e
  • A
  • Ψ
  • V
  • Ψ
  • r¯
  • t

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